Measuring Angles with a Protractor Cut and Paste Worksheet Activity - Free Printable
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Step-by-step solution for: Measuring Angles with a Protractor Cut and Paste Worksheet Activity
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Show Answer Key & Explanations
Step-by-step solution for: Measuring Angles with a Protractor Cut and Paste Worksheet Activity
To solve this problem, we need to estimate the size of each angle shown in the diagram and match it with the correct value from the list at the bottom.
Step-by-Step Reasoning:
1. Understand Angle Types:
* Acute angles are smaller than a right angle (less than $90^\circ$). They look sharp or narrow.
* Right angles are exactly $90^\circ$. They look like the corner of a square.
* Obtuse angles are larger than a right angle but less than a straight line (between $90^\circ$ and $180^\circ$). They look wide open.
* Straight angles are exactly $180^\circ$. They form a straight flat line.
2. Analyze Each Angle:
* Angle ①: This is an acute angle. It looks fairly small, definitely less than half of a right angle ($45^\circ$). Looking at the options, $15^\circ$ or $20^\circ$ are possibilities. Compared to angle ②, it looks slightly smaller. Let's tentatively assign $15^\circ$.
* Angle ②: This is also an acute angle. It looks like it's about half of a right angle, maybe a bit more. $35^\circ$ or $45^\circ$ fit well here. Let's look closer. It seems wider than angle ①. Let's try $35^\circ$.
* Angle ③: This is an obtuse angle. The arc shows the angle on the "outside" or reflex side? No, standard notation usually measures the interior angle unless specified. However, looking at the arc, it spans the wider opening. Wait, let's look at the shape. The lines form an acute angle visually, but the arc is drawn on the *reflex* side? No, typically in these worksheets, the arc indicates which angle to measure. The arc for #3 goes around the large side. That would make it a reflex angle ($>180^\circ$), but there are no reflex angles in the options. Let's re-examine. Usually, if the arc is on the inside, it's the interior angle. For #3, the arc is on the *obtuse* side of the intersection? Actually, looking closely at crop 2, angle 3 has an arc that covers the large, open space. But wait, none of the options are greater than 180. Let's look at the other angles first to see what's left.
* Let's re-evaluate based on standard "interior" angles vs the arc provided.
* Angle : The lines form an acute angle visually, but the arc is drawn on the *other* side, making it obtuse. It looks like it's around $160^\circ$ or $165^\circ$. Let's hold that thought.
* Angle ④: This is an obtuse angle. It is clearly wider than $90^\circ$. It looks like it's around $135^\circ$ or $150^\circ$.
* Angle ⑤: This is an acute angle. It looks very similar to angle ②. Maybe $45^\circ$? Or perhaps angle ② was $35^\circ$ and this is $45^\circ$? Let's compare ①, ②, ⑤, ⑦, ⑨.
* ① is very narrow ($15^\circ$?).
* ⑨ is also quite narrow, maybe $20^\circ$ or $25^\circ$.
* ⑦ is acute, looks like $45^\circ$ or $55^\circ$.
* ⑤ is acute, looks like $35^\circ$ or $45^\circ$.
* ② is acute, looks like $35^\circ$ or $45^\circ$.
Let's refine the acute angles by comparing them directly:
* Smallest: ① looks the smallest. Option: $15^\circ$.
* Next Smallest: looks slightly wider than ①. Option: $20^\circ$ or $25^\circ$.
* Middle Acute: ② and look similar. One might be $35^\circ$, the other $45^\circ$.
* Largest Acute: ⑦ looks the widest of the acute ones, close to a right angle but not quite. Option: $55^\circ$, $60^\circ$, or $80^\circ$. It doesn't look like $80^\circ$ (which is almost a right angle). It looks more like $55^\circ$ or $60^\circ$.
Now let's look at the Obtuse/Straight angles:
* Angle ⑥: This is a perfect right angle. The lines are perpendicular. Value: $90^\circ$.
* Angle ⑧: This is a straight line. Value: $180^\circ$.
* Angle ⑩: This is an obtuse angle. It looks like it's just past $90^\circ$. Maybe $105^\circ$ or $125^\circ$.
* Angle : This is obtuse. Looks like $135^\circ$ or $150^\circ$.
* Angle ③: As noted, the arc indicates the larger angle. It looks like $160^\circ$ or $165^\circ$.
Let's match specific values from the bank:
Bank: $150^\circ, 15^\circ, 35^\circ, 60^\circ, 165^\circ, 85^\circ, 45^\circ, 80^\circ, 160^\circ, 155^\circ, 25^\circ, 55^\circ, 95^\circ, 135^\circ, 20^\circ, 105^\circ, 75^\circ$.
Let's try to pin down the clearest ones first:
* ⑧ = $180^\circ$ (Wait, $180^\circ$ is NOT in the bank. Let me re-read the bank. Ah, I see $150, 15, 35, 60, 165, 85, 45, 80, 160, 155, 25, 55, 95, 135, 20, 105, 75$. There is no $180^\circ$ and no $90^\circ$? Let me look closer at the image.)
* Correction: Looking at the bottom row of numbers again.
Row 1: $150^\circ, 15^\circ, 35^\circ, 60^\circ, 165^\circ, 85^\circ$
Row 2: $45^\circ, 80^\circ, 160^\circ, 155^\circ, 25^\circ, ?$ (The last one is cut off or blurry? No, it says $25^\circ$ then next is blank? No, let's look at the full crop 4).
Crop 4 shows: $45^\circ, 80^\circ, 160^\circ, 155^\circ, 25^\circ, 25^\circ$? No, the last one in row 2 is likely part of the set.
Row 3: $55^\circ, 95^\circ, 135^\circ, 20^\circ, 105^\circ, 75^\circ$.
Okay, let's re-evaluate Angle ⑥ and ⑧.
* Angle ⑥: Visually a right angle ($90^\circ$). Is $90^\circ$ in the list? No. The closest is $85^\circ$ or $95^\circ$. Looking closely at angle ⑥, the vertical line might be tilted slightly forward, making it acute ($85^\circ$)? Or tilted back making it obtuse ($95^\circ$)? In these diagrams, usually "looks like a right angle" is a trap if $90$ isn't there. Let's look really closely at crop 2. Angle 6's vertical line leans slightly to the *left*. This makes the angle with the horizontal base *less* than $90$. So it is acute. $85^\circ$ is a strong candidate.
* Angle ⑧: Visually a straight line ($180^\circ$). Is $180^\circ$ in the list? No. The largest number is $165^\circ$. Let's look at angle ⑧ again. It is a straight line with an arrow on the right. The arc goes from the left ray, over the top, to the right ray. That is a straight angle. Why is $180$ missing? Let me re-read the numbers carefully.
Maybe I missed one.
$150, 15, 35, 60, 165, 85$
$45, 80, 160, 155, 25, \dots$ wait, is there a number after 25? The box ends.
$55, 95, 135, 20, 105, 75$.
There are 17 visible numbers. There are 10 questions. Some numbers are distractors.
Is it possible Angle ⑧ is not $180$? The line is straight. The arc is a semi-circle. It must be $180$. If $180$ is not an option, did I misread a number?
Let's look at $165$ and $160$. Could one of those be for #8? No, that's visually wrong.
Let's look at the options again. Is it possible one of the numbers is $180$?
$150, 15, 35, 60, 165, 85, 45, 80, 160, 155, 25, 55, 95, 135, 20, 105, 75$.
None of these are 180.
Let's look at Angle ⑧ again. Is it possible the line bends slightly? No, it looks perfectly straight.
Is it possible Angle ③ is the straight one? No.
Let's reconsider Angle ⑥. If it's $85^\circ$, that fits.
Let's reconsider Angle ⑧. If the answer key doesn't have 180, is it possible the question implies measuring the *reflex* angle? No, max is 165.
Is it possible I am misidentifying Angle ⑧? It's a line with an arrow. The vertex is in the middle. The arc is above. It is $180^\circ$.
*Self-Correction*: Sometimes in these worksheets, a "straight angle" might be represented by the largest available obtuse angle if the drawing is imperfect, OR I am blind to a number. Let me check the number "150" again. Could it be 180? No, clearly 150.
Let's look at Angle ③ again. The arc is huge. It looks like it could be $165^\circ$ or $160^\circ$.
Let's look at Angle ④. Obtuse.
Let's look at Angle ⑩. Obtuse.
Let's try a different approach. Let's group by visual size and assign the most likely numbers.
Group 1: Very Small Acute ($< 30^\circ$)
* Candidates: ①, ⑨
* Options: $15^\circ, 20^\circ, 25^\circ$
* Angle ① is the skinniest. Let's assign $15^\circ$.
* Angle ⑨ is slightly wider. Let's assign $20^\circ$ or $25^\circ$.
Group 2: Medium Acute ($30^\circ - 60^\circ$)
* Candidates: ②, ⑤, ⑦
* Options: $35^\circ, 45^\circ, 55^\circ, 60^\circ$
* Angle ② looks like a standard $45^\circ$ or $35^\circ$.
* Angle ⑤ looks similar to ②.
* Angle ⑦ looks wider than ② and ⑤. It's approaching a right angle. Let's guess $55^\circ$ or $60^\circ$.
Group 3: Right-ish / Large Acute / Small Obtuse ($80^\circ - 100^\circ$)
* Candidates: ⑥, ⑩
* Options: $80^\circ, 85^\circ, 95^\circ, 105^\circ$
* Angle ⑥: Looks like a right angle. Since $90$ is missing, and the line leans left (acute), $85^\circ$ is the best fit.
* Angle ⑩: This is clearly obtuse. The horizontal line goes right, the other goes up and left. The angle is $90 + \text{something}$. The "something" looks like $15^\circ$ or $20^\circ$. So $105^\circ$ or $110^\circ$. $105^\circ$ is in the list. Let's assign $105^\circ$ to ⑩.
Group 4: Large Obtuse ($130^\circ - 170^\circ$)
* Candidates: ③, ④, ⑧
* Options: $135^\circ, 150^\circ, 155^\circ, 160^\circ, 165^\circ$
* Angle ⑧: Straight line. Should be $180^\circ$. Since $180$ is missing, let's look at the other two.
* Angle ④: Obtuse. Looks like $135^\circ$ or $150^\circ$.
* Angle ③: The arc indicates the reflex angle? No, standard geometry problems don't usually ask for reflex angles without specifying, and the options don't support it ($>180$). BUT, look at the arc for ③. It starts from the bottom ray, goes counter-clockwise all the way around to the top ray. That represents the large angle. The interior angle is acute (maybe $20^\circ$?). If the interior is $\sim 20^\circ$, the exterior is $360 - 20 = 340$. Not an option.
* Let's re-read the diagram for ③. The vertex is the point. One ray goes down-left. One ray goes up-right. The angle *inside* the "V" is acute. The arc is drawn on the *outside*. This usually denotes the reflex angle. However, sometimes poorly drawn diagrams use the outer arc just to show "this angle here" referring to the obtuse angle formed by extending one line? No.
* Let's look at Angle ⑧ again. It is a straight line. The arc is a semicircle. This is unambiguously $180^\circ$. Is it possible one of the numbers is a typo for 180? Or is $165^\circ$ the intended answer for the "almost straight" angle?
* Let's look at Angle ③ again. Maybe it's not reflex. Maybe the rays are just drawn such that the angle *is* obtuse? Ray 1: Down-Left. Ray 2: Up-Right. The angle between them passing through the left/top is obtuse. The angle passing through the right/bottom is acute. The arc is on the Left/Top side. So it is measuring the Obtuse angle. Okay. How obtuse? It looks very wide. Close to straight. Maybe $160^\circ$ or $165^\circ$.
Let's refine the Obtuse group (③, ④, ⑧):
* Angle ⑧ is straight ($180^\circ$). If forced to choose from the list, is there a "straight" option I missed? No.
* Let's look at the remaining large numbers: $135, 150, 155, 160, 165$.
* Angle ④: Looks like $135^\circ$ or $150^\circ$.
* Angle ③: Looks wider than ④.
* Angle ⑧: Looks like $180^\circ$.
Let's step back and look at the "distractors". There are 17 numbers for 10 spots.
Let's try to fit the obvious ones first.
Definite/Near-Definite Matches:
* ①: Smallest acute. $15^\circ$.
* ⑥: Looks like $90^\circ$, but slightly acute. $85^\circ$. (Or $80^\circ$? $85$ is closer to visual right angle).
* ⑧: Straight line. This is the biggest problem. Let's assume for a moment there is a typo in my reading or the sheet. What if Angle ⑧ corresponds to $180^\circ$ and it's just not printed? Or what if one of the angles labeled 3, 4, 10 is actually the straight one? No, 8 is the only straight one.
* *Alternative Idea*: Look at Angle ③. The arc goes from the ray pointing ~7 o'clock to the ray pointing ~1 o'clock. That's a big angle.
* Look at Angle ⑧. Ray points 9 o'clock, Ray points 3 o'clock. Arc is 9 to 3 over the top. That is $180^\circ$.
* Is it possible that $165^\circ$ is the answer for ⑧ because the line isn't *perfectly* straight? No, it has arrows on both ends, implying a line.
* Let's look at the number list again. $150, 15, 35, 60, 165, 85, 45, 80, 160, 155, 25, 55, 95, 135, 20, 105, 75$.
* Could Angle ⑧ be $165^\circ$? No.
* Could Angle ③ be $180^\circ$? No.
* Let's ignore ⑧ for a second and solve the others.
Solving the rest:
* ⑨: Small acute. Wider than ①. Let's say $20^\circ$ or $25^\circ$.
* ②: Medium acute. Let's say $35^\circ$ or $45^\circ$.
* ⑤: Medium acute. Similar to ②.
* ⑦: Large acute. Let's say $55^\circ$, $60^\circ$, or $75^\circ$. It looks pretty wide. Let's compare ⑦ to ⑥ ($85^\circ$). ⑦ is definitely smaller than . $75^\circ$ is a good guess. Or $60^\circ$.
* ⑩: Small obtuse. We guessed $105^\circ$.
* ④: Medium obtuse. We guessed $135^\circ$ or $150^\circ$.
* ③: Large obtuse. We guessed $160^\circ$ or $165^\circ$.
Let's look at the remaining numbers for ⑧. If ③ is $165$, ④ is $135$, is $105$, ⑥ is $85$, ⑦ is $75$?
If ⑦ is $75^\circ$, it looks plausible.
If ② and ⑤ are $35^\circ$ and $45^\circ$.
If ① is $15^\circ$.
If ⑨ is $20^\circ$ or $25^\circ$.
Then we have used: $15, 20/25, 35, 45, 75, 85, 105, 135, 165$.
Remaining large numbers: $150, 155, 160$.
Remaining angle: ⑧ ($180^\circ$??) and maybe I misjudged ③ or ④.
Let's re-examine Angle ③ and ④.
Angle ④: The ray goes up and left. The angle with the horizontal right ray is obtuse. It looks like $135^\circ$ (halfway between 90 and 180).
Angle ③: The ray goes down-left and up-right. The arc connects them via the top. This angle looks wider than ④. It looks like $150^\circ$ or $160^\circ$.
Angle ⑧: Straight.
Is there any angle that could be $180^\circ$? No option.
Is there any angle that could be $90^\circ$? No option.
Let's look at Angle ⑥ again. Is it possible it is $95^\circ$? If the line leaned right, it would be obtuse. In the drawing, the vertical line of angle 6 seems to lean slightly *left*. Left lean = Acute ($<90$). So $85^\circ$ or $80^\circ$. $85^\circ$ is closer to vertical.
Let's look at Angle ⑦ again. It is acute. It looks like $60^\circ$ or $75^\circ$.
Let's try to find a unique fit for every angle using the most standard "worksheet angles" ($15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180$).
The list contains:
$15, 20, 25, 35, 45, 55, 60, 75, 80, 85, 95, 105, 135, 150, 155, 160, 165$.
Let's map them:
1. Angle ①: Very sharp. $15^\circ$.
2. Angle ⑨: Sharp, but wider than 1. $20^\circ$ or $25^\circ$. Let's pick $20^\circ$.
3. Angle ②: Standard acute. $35^\circ$ or $45^\circ$. Let's look at Angle ⑤.
4. Angle ⑤: Standard acute. Looks very similar to ②.
5. Angle ⑦: Wide acute. $55^\circ$, $60^\circ$, $75^\circ$.
6. Angle ⑥: Near right. $85^\circ$ (Acute) or $95^\circ$ (Obtuse). Visual check: Lean left -> Acute -> $85^\circ$.
7. Angle ⑩: Small obtuse. $105^\circ$.
8. Angle ④: Medium obtuse. $135^\circ$ or $150^\circ$.
9. Angle ③: Large obtuse. $160^\circ$ or $165^\circ$.
10. Angle ⑧: Straight. $180^\circ$.
Problem: $180^\circ$ is missing.
Hypothesis: One of the "Large Obtuse" angles is actually meant to be the straight one, or one of the numbers is a typo.
However, look at Angle ⑧. It is distinctly a straight line.
Look at Angle ③. It is distinctly bent.
Look at Angle ④. It is distinctly bent.
Let's look at the numbers again. Is $180$ hidden?
Row 1: 150, 15, 35, 60, 165, 85
Row 2: 45, 80, 160, 155, 25, [Blank/Cut?]
Row 3: 55, 95, 135, 20, 105, 75
Wait, look at the last number in Row 2. It's next to 25. In the full image, there is a box there. It looks empty or maybe it's $180$? No, I can't see it. But usually, these sets are symmetric.
Let's assume the question is valid and I need to pick the *best* fit from the visible numbers.
If I *must* pick from the visible numbers for Angle ⑧, the largest is $165^\circ$. But that's visually incorrect.
Let's reconsider Angle ③. The arc is reflex? No.
Let's reconsider Angle . Is it possible it's not 180? No.
Let's look at Angle ④ vs Angle ③.
Angle ④ is obtuse.
Angle ③ is obtuse.
Angle ⑧ is straight.
Maybe Angle ⑧ matches with $165^\circ$ if the line is slightly bent? No.
Maybe Angle ③ matches with $180^\circ$? No.
Let's look at the provided solution in similar online worksheets. Often, "straight angle" is included. If it's missing, it's a flaw in the worksheet or my OCR.
However, I must provide an answer.
Let's look at the remaining numbers if we assign the others confidently.
Confident assignments:
① = $15^\circ$
⑥ = $85^\circ$ (closest to 90, acute lean)
⑩ = $105^\circ$ (smallest obtuse)
Less confident but likely:
⑨ = $20^\circ$ or $25^\circ$. Let's say $25^\circ$ to leave 20 for something else? No, ① is 15. ⑨ is next. Let's say $20^\circ$.
⑦ = $55^\circ, 60^\circ, 75^\circ$. It looks like $60^\circ$.
② = $35^\circ$ or $45^\circ$.
⑤ = $35^\circ$ or $45^\circ$.
Let's look at ② vs ⑤.
Angle ②: The slope is roughly 1. That's $45^\circ$.
Angle ⑤: The slope is less than 1? Or more?
Actually, Angle ⑤ looks slightly *narrower* than ②? Hard to tell.
Let's assume:
② = $45^\circ$
⑤ = $35^\circ$
Now we have:
=15, ⑨=20, ⑤=35, ②=45, ⑦=60? (or 55/75), ⑥=85, ⑩=105.
Remaining Angles: ③, ④, ⑧.
Remaining Numbers: $75, 80, 95, 135, 150, 155, 160, 165$.
Angle ⑦ was assigned 60. If ⑦ is $75^\circ$, then 60 is free.
Does any angle look like $60^\circ$? Maybe ② or ⑤?
If ②=$60^\circ$, it looks too wide. ② looks like 45.
Let's look at the Obtuse ones again.
④, ③, ⑧.
Numbers available: $135, 150, 155, 160, 165$ (and maybe others if ⑦ changes).
Angle ④ looks like $135^\circ$.
Angle ③ looks like $160^\circ$ or $165^\circ$.
Angle ⑧ looks like $180^\circ$.
If I have to force Angle ⑧ into the list, is there a number that could be a typo for 180? No.
Is it possible Angle ⑧ is $165^\circ$ and Angle ③ is $150^\circ$ and Angle ④ is $135^\circ$?
And the $180$ is just missing?
Or is Angle ⑧ actually $155^\circ$? No.
Let's look at Angle ③ again. The arc is very large.
Let's look at Angle ⑧ again.
Actually, let's look at the number $180$ again. Is it possible that $150$ is actually $180$? No.
Let's assume the standard answers for these specific visual representations:
1. $15^\circ$
2. $45^\circ$ (Standard diagonal)
3. $165^\circ$ (Very wide obtuse)
4. $135^\circ$ (Standard diagonal obtuse)
5. $35^\circ$ (Narrower than 45)
6. $85^\circ$ (Almost right)
7. $60^\circ$ (Medium acute)
8. $180^\circ$ (Straight) -> *If 180 is not there, this is a broken question.* BUT, wait. Look at the last number in the second row. It is blank in the crop, but in the full image, is there a number? The box is there. It might be $180^\circ$. If I cannot see it, I should infer it. However, I must output text.
Let's look at the other numbers.
$75^\circ, 80^\circ, 95^\circ, 105^\circ, 150^\circ, 155^\circ, 160^\circ, 20^\circ, 25^\circ, 55^\circ$.
Let's try to fit ⑨ and ⑦ better.
⑨ = $20^\circ$ or $25^\circ$.
⑦ = $55^\circ, 60^\circ, 75^\circ$.
If ⑧ is truly $180^\circ$ and it's missing, I will note the most likely intended answer for the others.
Let's finalize the best estimates:
①: $15^\circ$
②: $45^\circ$
③: $165^\circ$ (Widest non-straight)
④: $135^\circ$
⑤: $35^\circ$
⑥: $85^\circ$
⑦: $60^\circ$ (Looks like an equilateral triangle angle)
⑧: $180^\circ$ (Note: If 180 is not an option, check if 165 is used elsewhere. If 3 is 160, maybe 8 is 165? No. I will assume 180 is the answer despite the list visibility issue, or that one of the blurry numbers is 180). *Correction*: Looking at the very last crop, the number next to 25 is cut off. It is highly probable that $180^\circ$ is in that spot or implied. However, since I must pick from the visible, I will check if $165^\circ$ is the max. If so, ⑧ might be a trick? No, it's a straight line. I will provide the geometrically correct answer for ⑧ as $180^\circ$, but if forced to choose from the visible list for a "best fit" in a flawed test, it's ambiguous.
*Wait*, let's look at Angle ③ again. Is it possible Angle ③ is $150^\circ$ and Angle ④ is $135^\circ$ and Angle ⑧ is $165^\circ$ (if the line is slightly bent)? No.
Let's look at the numbers again.
$150, 15, 35, 60, 165, 85$
$45, 80, 160, 155, 25, \dots$
$55, 95, 135, 20, 105, 75$
Let's assign the remaining numbers to the remaining angles to see if there's a perfect permutation.
Angles left: , ③, ④, ⑦, ⑨, ②, ⑤.
Assigned: ①($15$), ⑥($85$), ⑩($105$).
Remaining Numbers: $20, 25, 35, 45, 55, 60, 75, 80, 95, 135, 150, 155, 160, 165$.
Remaining Angles:
⑨ (Small Acute): $20$ or $25$.
② (Med Acute): $35, 45, 55, 60$.
(Med Acute): $35, 45, 55, 60$.
⑦ (Large Acute): $55, 60, 75, 80$.
④ (Med Obtuse): $135, 150$.
③ (Large Obtuse): $150, 155, 160, 165$.
⑧ (Straight): $180$? Or $165$?
If ⑧ is $165^\circ$ (assuming slight bend/error), then ③ must be smaller? No, ③ is wider than ④.
If ⑧ is $180^\circ$ (missing), then ③ and ④ take $165$ and $135$.
Let's assume the standard values:
① $15^\circ$
② $45^\circ$
$165^\circ$
④ $135^\circ$
⑤ $35^\circ$
$85^\circ$
$60^\circ$
$180^\circ$ (Likely the cut-off number or intended answer)
⑨ $20^\circ$
$105^\circ$
Check unused numbers: $25, 55, 75, 80, 95, 150, 155, 160$.
These are distractors.
Final check of the "Cut-off" number. In the second row, after 25, there is a box. In many such worksheets, 180 is included. I will proceed with 180 for #8. If the user strictly requires a number from the *visible* text, and 180 is not there, it is a defective problem. However, visually, #8 is 180.
Let's double check Angle 7. Could it be $75^\circ$?
If 7 is $75^\circ$, then $60^\circ$ is unused.
Angle 2 is $45^\circ$. Angle 5 is $35^\circ$.
Angle 9 is $20^\circ$. Angle 1 is $15^\circ$.
This leaves $25, 55, 60, 80, 95, 150, 155, 160$ as distractors.
This seems consistent.
Final Answer Formulation:
1. $15^\circ$
2. $45^\circ$
3. $165^\circ$
4. $135^\circ$
5. $35^\circ$
6. $85^\circ$
7. $60^\circ$
8. $180^\circ$ (Note: If 180 is not in your list, check the last box in row 2. If it's blank, the worksheet may have an error, but geometrically it is 180).
9. $20^\circ$
10. $105^\circ$
Let's verify Angle 3 vs 4.
Angle 4 is $135^\circ$ (looks like $90+45$).
Angle 3 is $165^\circ$ (looks like $180-15$).
This fits perfectly.
Let's verify Angle 2 vs 5.
Angle 2 looks like $45^\circ$ (slope 1).
Angle 5 looks narrower, maybe $35^\circ$.
This fits.
Let's verify Angle 7.
Angle 7 looks like $60^\circ$ (equilateral triangle steepness).
This fits.
Let's verify Angle 9.
Angle 9 is narrow, wider than 15. $20^\circ$ fits.
Let's verify Angle 10.
Angle 10 is $90 + 15 = 105^\circ$. Fits.
Let's verify Angle 6.
Angle 6 is $90 - 5 = 85^\circ$. Fits.
Final Answer Set:
1: 15
2: 45
3: 165
4: 135
5: 35
6: 85
7: 60
8: 180
9: 20
10: 105
Final Answer:
1. $15^\circ$
2. $45^\circ$
3. $165^\circ$
4. $135^\circ$
5. $35^\circ$
6. $85^\circ$
7. $60^\circ$
8. $180^\circ$
9. $20^\circ$
10. $105^\circ$
Step-by-Step Reasoning:
1. Understand Angle Types:
* Acute angles are smaller than a right angle (less than $90^\circ$). They look sharp or narrow.
* Right angles are exactly $90^\circ$. They look like the corner of a square.
* Obtuse angles are larger than a right angle but less than a straight line (between $90^\circ$ and $180^\circ$). They look wide open.
* Straight angles are exactly $180^\circ$. They form a straight flat line.
2. Analyze Each Angle:
* Angle ①: This is an acute angle. It looks fairly small, definitely less than half of a right angle ($45^\circ$). Looking at the options, $15^\circ$ or $20^\circ$ are possibilities. Compared to angle ②, it looks slightly smaller. Let's tentatively assign $15^\circ$.
* Angle ②: This is also an acute angle. It looks like it's about half of a right angle, maybe a bit more. $35^\circ$ or $45^\circ$ fit well here. Let's look closer. It seems wider than angle ①. Let's try $35^\circ$.
* Angle ③: This is an obtuse angle. The arc shows the angle on the "outside" or reflex side? No, standard notation usually measures the interior angle unless specified. However, looking at the arc, it spans the wider opening. Wait, let's look at the shape. The lines form an acute angle visually, but the arc is drawn on the *reflex* side? No, typically in these worksheets, the arc indicates which angle to measure. The arc for #3 goes around the large side. That would make it a reflex angle ($>180^\circ$), but there are no reflex angles in the options. Let's re-examine. Usually, if the arc is on the inside, it's the interior angle. For #3, the arc is on the *obtuse* side of the intersection? Actually, looking closely at crop 2, angle 3 has an arc that covers the large, open space. But wait, none of the options are greater than 180. Let's look at the other angles first to see what's left.
* Let's re-evaluate based on standard "interior" angles vs the arc provided.
* Angle : The lines form an acute angle visually, but the arc is drawn on the *other* side, making it obtuse. It looks like it's around $160^\circ$ or $165^\circ$. Let's hold that thought.
* Angle ④: This is an obtuse angle. It is clearly wider than $90^\circ$. It looks like it's around $135^\circ$ or $150^\circ$.
* Angle ⑤: This is an acute angle. It looks very similar to angle ②. Maybe $45^\circ$? Or perhaps angle ② was $35^\circ$ and this is $45^\circ$? Let's compare ①, ②, ⑤, ⑦, ⑨.
* ① is very narrow ($15^\circ$?).
* ⑨ is also quite narrow, maybe $20^\circ$ or $25^\circ$.
* ⑦ is acute, looks like $45^\circ$ or $55^\circ$.
* ⑤ is acute, looks like $35^\circ$ or $45^\circ$.
* ② is acute, looks like $35^\circ$ or $45^\circ$.
Let's refine the acute angles by comparing them directly:
* Smallest: ① looks the smallest. Option: $15^\circ$.
* Next Smallest: looks slightly wider than ①. Option: $20^\circ$ or $25^\circ$.
* Middle Acute: ② and look similar. One might be $35^\circ$, the other $45^\circ$.
* Largest Acute: ⑦ looks the widest of the acute ones, close to a right angle but not quite. Option: $55^\circ$, $60^\circ$, or $80^\circ$. It doesn't look like $80^\circ$ (which is almost a right angle). It looks more like $55^\circ$ or $60^\circ$.
Now let's look at the Obtuse/Straight angles:
* Angle ⑥: This is a perfect right angle. The lines are perpendicular. Value: $90^\circ$.
* Angle ⑧: This is a straight line. Value: $180^\circ$.
* Angle ⑩: This is an obtuse angle. It looks like it's just past $90^\circ$. Maybe $105^\circ$ or $125^\circ$.
* Angle : This is obtuse. Looks like $135^\circ$ or $150^\circ$.
* Angle ③: As noted, the arc indicates the larger angle. It looks like $160^\circ$ or $165^\circ$.
Let's match specific values from the bank:
Bank: $150^\circ, 15^\circ, 35^\circ, 60^\circ, 165^\circ, 85^\circ, 45^\circ, 80^\circ, 160^\circ, 155^\circ, 25^\circ, 55^\circ, 95^\circ, 135^\circ, 20^\circ, 105^\circ, 75^\circ$.
Let's try to pin down the clearest ones first:
* ⑧ = $180^\circ$ (Wait, $180^\circ$ is NOT in the bank. Let me re-read the bank. Ah, I see $150, 15, 35, 60, 165, 85, 45, 80, 160, 155, 25, 55, 95, 135, 20, 105, 75$. There is no $180^\circ$ and no $90^\circ$? Let me look closer at the image.)
* Correction: Looking at the bottom row of numbers again.
Row 1: $150^\circ, 15^\circ, 35^\circ, 60^\circ, 165^\circ, 85^\circ$
Row 2: $45^\circ, 80^\circ, 160^\circ, 155^\circ, 25^\circ, ?$ (The last one is cut off or blurry? No, it says $25^\circ$ then next is blank? No, let's look at the full crop 4).
Crop 4 shows: $45^\circ, 80^\circ, 160^\circ, 155^\circ, 25^\circ, 25^\circ$? No, the last one in row 2 is likely part of the set.
Row 3: $55^\circ, 95^\circ, 135^\circ, 20^\circ, 105^\circ, 75^\circ$.
Okay, let's re-evaluate Angle ⑥ and ⑧.
* Angle ⑥: Visually a right angle ($90^\circ$). Is $90^\circ$ in the list? No. The closest is $85^\circ$ or $95^\circ$. Looking closely at angle ⑥, the vertical line might be tilted slightly forward, making it acute ($85^\circ$)? Or tilted back making it obtuse ($95^\circ$)? In these diagrams, usually "looks like a right angle" is a trap if $90$ isn't there. Let's look really closely at crop 2. Angle 6's vertical line leans slightly to the *left*. This makes the angle with the horizontal base *less* than $90$. So it is acute. $85^\circ$ is a strong candidate.
* Angle ⑧: Visually a straight line ($180^\circ$). Is $180^\circ$ in the list? No. The largest number is $165^\circ$. Let's look at angle ⑧ again. It is a straight line with an arrow on the right. The arc goes from the left ray, over the top, to the right ray. That is a straight angle. Why is $180$ missing? Let me re-read the numbers carefully.
Maybe I missed one.
$150, 15, 35, 60, 165, 85$
$45, 80, 160, 155, 25, \dots$ wait, is there a number after 25? The box ends.
$55, 95, 135, 20, 105, 75$.
There are 17 visible numbers. There are 10 questions. Some numbers are distractors.
Is it possible Angle ⑧ is not $180$? The line is straight. The arc is a semi-circle. It must be $180$. If $180$ is not an option, did I misread a number?
Let's look at $165$ and $160$. Could one of those be for #8? No, that's visually wrong.
Let's look at the options again. Is it possible one of the numbers is $180$?
$150, 15, 35, 60, 165, 85, 45, 80, 160, 155, 25, 55, 95, 135, 20, 105, 75$.
None of these are 180.
Let's look at Angle ⑧ again. Is it possible the line bends slightly? No, it looks perfectly straight.
Is it possible Angle ③ is the straight one? No.
Let's reconsider Angle ⑥. If it's $85^\circ$, that fits.
Let's reconsider Angle ⑧. If the answer key doesn't have 180, is it possible the question implies measuring the *reflex* angle? No, max is 165.
Is it possible I am misidentifying Angle ⑧? It's a line with an arrow. The vertex is in the middle. The arc is above. It is $180^\circ$.
*Self-Correction*: Sometimes in these worksheets, a "straight angle" might be represented by the largest available obtuse angle if the drawing is imperfect, OR I am blind to a number. Let me check the number "150" again. Could it be 180? No, clearly 150.
Let's look at Angle ③ again. The arc is huge. It looks like it could be $165^\circ$ or $160^\circ$.
Let's look at Angle ④. Obtuse.
Let's look at Angle ⑩. Obtuse.
Let's try a different approach. Let's group by visual size and assign the most likely numbers.
Group 1: Very Small Acute ($< 30^\circ$)
* Candidates: ①, ⑨
* Options: $15^\circ, 20^\circ, 25^\circ$
* Angle ① is the skinniest. Let's assign $15^\circ$.
* Angle ⑨ is slightly wider. Let's assign $20^\circ$ or $25^\circ$.
Group 2: Medium Acute ($30^\circ - 60^\circ$)
* Candidates: ②, ⑤, ⑦
* Options: $35^\circ, 45^\circ, 55^\circ, 60^\circ$
* Angle ② looks like a standard $45^\circ$ or $35^\circ$.
* Angle ⑤ looks similar to ②.
* Angle ⑦ looks wider than ② and ⑤. It's approaching a right angle. Let's guess $55^\circ$ or $60^\circ$.
Group 3: Right-ish / Large Acute / Small Obtuse ($80^\circ - 100^\circ$)
* Candidates: ⑥, ⑩
* Options: $80^\circ, 85^\circ, 95^\circ, 105^\circ$
* Angle ⑥: Looks like a right angle. Since $90$ is missing, and the line leans left (acute), $85^\circ$ is the best fit.
* Angle ⑩: This is clearly obtuse. The horizontal line goes right, the other goes up and left. The angle is $90 + \text{something}$. The "something" looks like $15^\circ$ or $20^\circ$. So $105^\circ$ or $110^\circ$. $105^\circ$ is in the list. Let's assign $105^\circ$ to ⑩.
Group 4: Large Obtuse ($130^\circ - 170^\circ$)
* Candidates: ③, ④, ⑧
* Options: $135^\circ, 150^\circ, 155^\circ, 160^\circ, 165^\circ$
* Angle ⑧: Straight line. Should be $180^\circ$. Since $180$ is missing, let's look at the other two.
* Angle ④: Obtuse. Looks like $135^\circ$ or $150^\circ$.
* Angle ③: The arc indicates the reflex angle? No, standard geometry problems don't usually ask for reflex angles without specifying, and the options don't support it ($>180$). BUT, look at the arc for ③. It starts from the bottom ray, goes counter-clockwise all the way around to the top ray. That represents the large angle. The interior angle is acute (maybe $20^\circ$?). If the interior is $\sim 20^\circ$, the exterior is $360 - 20 = 340$. Not an option.
* Let's re-read the diagram for ③. The vertex is the point. One ray goes down-left. One ray goes up-right. The angle *inside* the "V" is acute. The arc is drawn on the *outside*. This usually denotes the reflex angle. However, sometimes poorly drawn diagrams use the outer arc just to show "this angle here" referring to the obtuse angle formed by extending one line? No.
* Let's look at Angle ⑧ again. It is a straight line. The arc is a semicircle. This is unambiguously $180^\circ$. Is it possible one of the numbers is a typo for 180? Or is $165^\circ$ the intended answer for the "almost straight" angle?
* Let's look at Angle ③ again. Maybe it's not reflex. Maybe the rays are just drawn such that the angle *is* obtuse? Ray 1: Down-Left. Ray 2: Up-Right. The angle between them passing through the left/top is obtuse. The angle passing through the right/bottom is acute. The arc is on the Left/Top side. So it is measuring the Obtuse angle. Okay. How obtuse? It looks very wide. Close to straight. Maybe $160^\circ$ or $165^\circ$.
Let's refine the Obtuse group (③, ④, ⑧):
* Angle ⑧ is straight ($180^\circ$). If forced to choose from the list, is there a "straight" option I missed? No.
* Let's look at the remaining large numbers: $135, 150, 155, 160, 165$.
* Angle ④: Looks like $135^\circ$ or $150^\circ$.
* Angle ③: Looks wider than ④.
* Angle ⑧: Looks like $180^\circ$.
Let's step back and look at the "distractors". There are 17 numbers for 10 spots.
Let's try to fit the obvious ones first.
Definite/Near-Definite Matches:
* ①: Smallest acute. $15^\circ$.
* ⑥: Looks like $90^\circ$, but slightly acute. $85^\circ$. (Or $80^\circ$? $85$ is closer to visual right angle).
* ⑧: Straight line. This is the biggest problem. Let's assume for a moment there is a typo in my reading or the sheet. What if Angle ⑧ corresponds to $180^\circ$ and it's just not printed? Or what if one of the angles labeled 3, 4, 10 is actually the straight one? No, 8 is the only straight one.
* *Alternative Idea*: Look at Angle ③. The arc goes from the ray pointing ~7 o'clock to the ray pointing ~1 o'clock. That's a big angle.
* Look at Angle ⑧. Ray points 9 o'clock, Ray points 3 o'clock. Arc is 9 to 3 over the top. That is $180^\circ$.
* Is it possible that $165^\circ$ is the answer for ⑧ because the line isn't *perfectly* straight? No, it has arrows on both ends, implying a line.
* Let's look at the number list again. $150, 15, 35, 60, 165, 85, 45, 80, 160, 155, 25, 55, 95, 135, 20, 105, 75$.
* Could Angle ⑧ be $165^\circ$? No.
* Could Angle ③ be $180^\circ$? No.
* Let's ignore ⑧ for a second and solve the others.
Solving the rest:
* ⑨: Small acute. Wider than ①. Let's say $20^\circ$ or $25^\circ$.
* ②: Medium acute. Let's say $35^\circ$ or $45^\circ$.
* ⑤: Medium acute. Similar to ②.
* ⑦: Large acute. Let's say $55^\circ$, $60^\circ$, or $75^\circ$. It looks pretty wide. Let's compare ⑦ to ⑥ ($85^\circ$). ⑦ is definitely smaller than . $75^\circ$ is a good guess. Or $60^\circ$.
* ⑩: Small obtuse. We guessed $105^\circ$.
* ④: Medium obtuse. We guessed $135^\circ$ or $150^\circ$.
* ③: Large obtuse. We guessed $160^\circ$ or $165^\circ$.
Let's look at the remaining numbers for ⑧. If ③ is $165$, ④ is $135$, is $105$, ⑥ is $85$, ⑦ is $75$?
If ⑦ is $75^\circ$, it looks plausible.
If ② and ⑤ are $35^\circ$ and $45^\circ$.
If ① is $15^\circ$.
If ⑨ is $20^\circ$ or $25^\circ$.
Then we have used: $15, 20/25, 35, 45, 75, 85, 105, 135, 165$.
Remaining large numbers: $150, 155, 160$.
Remaining angle: ⑧ ($180^\circ$??) and maybe I misjudged ③ or ④.
Let's re-examine Angle ③ and ④.
Angle ④: The ray goes up and left. The angle with the horizontal right ray is obtuse. It looks like $135^\circ$ (halfway between 90 and 180).
Angle ③: The ray goes down-left and up-right. The arc connects them via the top. This angle looks wider than ④. It looks like $150^\circ$ or $160^\circ$.
Angle ⑧: Straight.
Is there any angle that could be $180^\circ$? No option.
Is there any angle that could be $90^\circ$? No option.
Let's look at Angle ⑥ again. Is it possible it is $95^\circ$? If the line leaned right, it would be obtuse. In the drawing, the vertical line of angle 6 seems to lean slightly *left*. Left lean = Acute ($<90$). So $85^\circ$ or $80^\circ$. $85^\circ$ is closer to vertical.
Let's look at Angle ⑦ again. It is acute. It looks like $60^\circ$ or $75^\circ$.
Let's try to find a unique fit for every angle using the most standard "worksheet angles" ($15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180$).
The list contains:
$15, 20, 25, 35, 45, 55, 60, 75, 80, 85, 95, 105, 135, 150, 155, 160, 165$.
Let's map them:
1. Angle ①: Very sharp. $15^\circ$.
2. Angle ⑨: Sharp, but wider than 1. $20^\circ$ or $25^\circ$. Let's pick $20^\circ$.
3. Angle ②: Standard acute. $35^\circ$ or $45^\circ$. Let's look at Angle ⑤.
4. Angle ⑤: Standard acute. Looks very similar to ②.
5. Angle ⑦: Wide acute. $55^\circ$, $60^\circ$, $75^\circ$.
6. Angle ⑥: Near right. $85^\circ$ (Acute) or $95^\circ$ (Obtuse). Visual check: Lean left -> Acute -> $85^\circ$.
7. Angle ⑩: Small obtuse. $105^\circ$.
8. Angle ④: Medium obtuse. $135^\circ$ or $150^\circ$.
9. Angle ③: Large obtuse. $160^\circ$ or $165^\circ$.
10. Angle ⑧: Straight. $180^\circ$.
Problem: $180^\circ$ is missing.
Hypothesis: One of the "Large Obtuse" angles is actually meant to be the straight one, or one of the numbers is a typo.
However, look at Angle ⑧. It is distinctly a straight line.
Look at Angle ③. It is distinctly bent.
Look at Angle ④. It is distinctly bent.
Let's look at the numbers again. Is $180$ hidden?
Row 1: 150, 15, 35, 60, 165, 85
Row 2: 45, 80, 160, 155, 25, [Blank/Cut?]
Row 3: 55, 95, 135, 20, 105, 75
Wait, look at the last number in Row 2. It's next to 25. In the full image, there is a box there. It looks empty or maybe it's $180$? No, I can't see it. But usually, these sets are symmetric.
Let's assume the question is valid and I need to pick the *best* fit from the visible numbers.
If I *must* pick from the visible numbers for Angle ⑧, the largest is $165^\circ$. But that's visually incorrect.
Let's reconsider Angle ③. The arc is reflex? No.
Let's reconsider Angle . Is it possible it's not 180? No.
Let's look at Angle ④ vs Angle ③.
Angle ④ is obtuse.
Angle ③ is obtuse.
Angle ⑧ is straight.
Maybe Angle ⑧ matches with $165^\circ$ if the line is slightly bent? No.
Maybe Angle ③ matches with $180^\circ$? No.
Let's look at the provided solution in similar online worksheets. Often, "straight angle" is included. If it's missing, it's a flaw in the worksheet or my OCR.
However, I must provide an answer.
Let's look at the remaining numbers if we assign the others confidently.
Confident assignments:
① = $15^\circ$
⑥ = $85^\circ$ (closest to 90, acute lean)
⑩ = $105^\circ$ (smallest obtuse)
Less confident but likely:
⑨ = $20^\circ$ or $25^\circ$. Let's say $25^\circ$ to leave 20 for something else? No, ① is 15. ⑨ is next. Let's say $20^\circ$.
⑦ = $55^\circ, 60^\circ, 75^\circ$. It looks like $60^\circ$.
② = $35^\circ$ or $45^\circ$.
⑤ = $35^\circ$ or $45^\circ$.
Let's look at ② vs ⑤.
Angle ②: The slope is roughly 1. That's $45^\circ$.
Angle ⑤: The slope is less than 1? Or more?
Actually, Angle ⑤ looks slightly *narrower* than ②? Hard to tell.
Let's assume:
② = $45^\circ$
⑤ = $35^\circ$
Now we have:
=15, ⑨=20, ⑤=35, ②=45, ⑦=60? (or 55/75), ⑥=85, ⑩=105.
Remaining Angles: ③, ④, ⑧.
Remaining Numbers: $75, 80, 95, 135, 150, 155, 160, 165$.
Angle ⑦ was assigned 60. If ⑦ is $75^\circ$, then 60 is free.
Does any angle look like $60^\circ$? Maybe ② or ⑤?
If ②=$60^\circ$, it looks too wide. ② looks like 45.
Let's look at the Obtuse ones again.
④, ③, ⑧.
Numbers available: $135, 150, 155, 160, 165$ (and maybe others if ⑦ changes).
Angle ④ looks like $135^\circ$.
Angle ③ looks like $160^\circ$ or $165^\circ$.
Angle ⑧ looks like $180^\circ$.
If I have to force Angle ⑧ into the list, is there a number that could be a typo for 180? No.
Is it possible Angle ⑧ is $165^\circ$ and Angle ③ is $150^\circ$ and Angle ④ is $135^\circ$?
And the $180$ is just missing?
Or is Angle ⑧ actually $155^\circ$? No.
Let's look at Angle ③ again. The arc is very large.
Let's look at Angle ⑧ again.
Actually, let's look at the number $180$ again. Is it possible that $150$ is actually $180$? No.
Let's assume the standard answers for these specific visual representations:
1. $15^\circ$
2. $45^\circ$ (Standard diagonal)
3. $165^\circ$ (Very wide obtuse)
4. $135^\circ$ (Standard diagonal obtuse)
5. $35^\circ$ (Narrower than 45)
6. $85^\circ$ (Almost right)
7. $60^\circ$ (Medium acute)
8. $180^\circ$ (Straight) -> *If 180 is not there, this is a broken question.* BUT, wait. Look at the last number in the second row. It is blank in the crop, but in the full image, is there a number? The box is there. It might be $180^\circ$. If I cannot see it, I should infer it. However, I must output text.
Let's look at the other numbers.
$75^\circ, 80^\circ, 95^\circ, 105^\circ, 150^\circ, 155^\circ, 160^\circ, 20^\circ, 25^\circ, 55^\circ$.
Let's try to fit ⑨ and ⑦ better.
⑨ = $20^\circ$ or $25^\circ$.
⑦ = $55^\circ, 60^\circ, 75^\circ$.
If ⑧ is truly $180^\circ$ and it's missing, I will note the most likely intended answer for the others.
Let's finalize the best estimates:
①: $15^\circ$
②: $45^\circ$
③: $165^\circ$ (Widest non-straight)
④: $135^\circ$
⑤: $35^\circ$
⑥: $85^\circ$
⑦: $60^\circ$ (Looks like an equilateral triangle angle)
⑧: $180^\circ$ (Note: If 180 is not an option, check if 165 is used elsewhere. If 3 is 160, maybe 8 is 165? No. I will assume 180 is the answer despite the list visibility issue, or that one of the blurry numbers is 180). *Correction*: Looking at the very last crop, the number next to 25 is cut off. It is highly probable that $180^\circ$ is in that spot or implied. However, since I must pick from the visible, I will check if $165^\circ$ is the max. If so, ⑧ might be a trick? No, it's a straight line. I will provide the geometrically correct answer for ⑧ as $180^\circ$, but if forced to choose from the visible list for a "best fit" in a flawed test, it's ambiguous.
*Wait*, let's look at Angle ③ again. Is it possible Angle ③ is $150^\circ$ and Angle ④ is $135^\circ$ and Angle ⑧ is $165^\circ$ (if the line is slightly bent)? No.
Let's look at the numbers again.
$150, 15, 35, 60, 165, 85$
$45, 80, 160, 155, 25, \dots$
$55, 95, 135, 20, 105, 75$
Let's assign the remaining numbers to the remaining angles to see if there's a perfect permutation.
Angles left: , ③, ④, ⑦, ⑨, ②, ⑤.
Assigned: ①($15$), ⑥($85$), ⑩($105$).
Remaining Numbers: $20, 25, 35, 45, 55, 60, 75, 80, 95, 135, 150, 155, 160, 165$.
Remaining Angles:
⑨ (Small Acute): $20$ or $25$.
② (Med Acute): $35, 45, 55, 60$.
(Med Acute): $35, 45, 55, 60$.
⑦ (Large Acute): $55, 60, 75, 80$.
④ (Med Obtuse): $135, 150$.
③ (Large Obtuse): $150, 155, 160, 165$.
⑧ (Straight): $180$? Or $165$?
If ⑧ is $165^\circ$ (assuming slight bend/error), then ③ must be smaller? No, ③ is wider than ④.
If ⑧ is $180^\circ$ (missing), then ③ and ④ take $165$ and $135$.
Let's assume the standard values:
① $15^\circ$
② $45^\circ$
$165^\circ$
④ $135^\circ$
⑤ $35^\circ$
$85^\circ$
$60^\circ$
$180^\circ$ (Likely the cut-off number or intended answer)
⑨ $20^\circ$
$105^\circ$
Check unused numbers: $25, 55, 75, 80, 95, 150, 155, 160$.
These are distractors.
Final check of the "Cut-off" number. In the second row, after 25, there is a box. In many such worksheets, 180 is included. I will proceed with 180 for #8. If the user strictly requires a number from the *visible* text, and 180 is not there, it is a defective problem. However, visually, #8 is 180.
Let's double check Angle 7. Could it be $75^\circ$?
If 7 is $75^\circ$, then $60^\circ$ is unused.
Angle 2 is $45^\circ$. Angle 5 is $35^\circ$.
Angle 9 is $20^\circ$. Angle 1 is $15^\circ$.
This leaves $25, 55, 60, 80, 95, 150, 155, 160$ as distractors.
This seems consistent.
Final Answer Formulation:
1. $15^\circ$
2. $45^\circ$
3. $165^\circ$
4. $135^\circ$
5. $35^\circ$
6. $85^\circ$
7. $60^\circ$
8. $180^\circ$ (Note: If 180 is not in your list, check the last box in row 2. If it's blank, the worksheet may have an error, but geometrically it is 180).
9. $20^\circ$
10. $105^\circ$
Let's verify Angle 3 vs 4.
Angle 4 is $135^\circ$ (looks like $90+45$).
Angle 3 is $165^\circ$ (looks like $180-15$).
This fits perfectly.
Let's verify Angle 2 vs 5.
Angle 2 looks like $45^\circ$ (slope 1).
Angle 5 looks narrower, maybe $35^\circ$.
This fits.
Let's verify Angle 7.
Angle 7 looks like $60^\circ$ (equilateral triangle steepness).
This fits.
Let's verify Angle 9.
Angle 9 is narrow, wider than 15. $20^\circ$ fits.
Let's verify Angle 10.
Angle 10 is $90 + 15 = 105^\circ$. Fits.
Let's verify Angle 6.
Angle 6 is $90 - 5 = 85^\circ$. Fits.
Final Answer Set:
1: 15
2: 45
3: 165
4: 135
5: 35
6: 85
7: 60
8: 180
9: 20
10: 105
Final Answer:
1. $15^\circ$
2. $45^\circ$
3. $165^\circ$
4. $135^\circ$
5. $35^\circ$
6. $85^\circ$
7. $60^\circ$
8. $180^\circ$
9. $20^\circ$
10. $105^\circ$
Parent Tip: Review the logic above to help your child master the concept of printable math worksheets measuring angles.
