Angle Word Problems - 4th Grade Math Worksheet | Teach Starter - Free Printable

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Here are the step-by-step solutions for the "Angle Word Problems – Multiple Choice" worksheet shown in the foreground.

Problem 1

Question: In triangle ABC, the measure of angle A is $25^\circ$ less than the size of angle B and the measure of angle C is $80^\circ$. What is the measurement of angle B?

Step-by-Step Solution:
1. We know the sum of angles in a triangle is always $180^\circ$. So, $A + B + C = 180^\circ$.
2. We are given that Angle $C = 80^\circ$.
3. We are given that Angle $A$ is $25^\circ$ less than Angle $B$. We can write this as: $A = B - 25$.
4. Substitute these values into the sum equation:
$(B - 25) + B + 80 = 180$
5. Combine like terms ($B + B = 2B$ and $-25 + 80 = 55$):
$2B + 55 = 180$
6. Subtract 55 from both sides:
$2B = 125$
7. Divide by 2:
$B = 62.5^\circ$

*Wait, looking at the options provided in the image (a. $59^\circ$, b. $55^\circ$, c. $63^\circ$, d. $54^\circ$), none match $62.5^\circ$ exactly. Let me re-read the text carefully.*

Let's look at Problem 4 on the same sheet, which seems to have identical text but different numbers. Let's look at Problem 1 again.
"In triangle ABC... measure of angle A is $25^\circ$ less than... angle B... angle C is $80^\circ$."
Calculation: $180 - 80 = 100$. So $A + B = 100$.
$A = B - 25$.
$(B - 25) + B = 100 \rightarrow 2B = 125 \rightarrow B = 62.5$.

Let's check the other problems to ensure I'm reading the blurry text correctly.
Problem 2: Right triangle DEF, angle E is right ($90^\circ$), angle F is $16^\circ$. Find D.
$180 - 90 - 16 = 74^\circ$. Option c is $74^\circ$. This matches.

Problem 3: Two angles inside a right triangle are $22^\circ$ and $90^\circ$. Find missing.
$180 - 90 - 22 = 68^\circ$. Option d is $68^\circ$. This matches.

Problem 5: Branch in tree, angle $49^\circ$. Measure of bottom angle?
This implies a straight line ($180^\circ$). $180 - 49 = 131^\circ$. Option b is $139^\circ$? No, option b is $139$, option d is $131$. Wait, let me look closer at crop 5.
Option a: $41$, b: $139$, c: $111$, d: $131$.
If it's supplementary, it's $131^\circ$. If it's complementary (right angle corner), it's $90-49=41^\circ$. The diagram usually shows a branch coming off a trunk. If it's an obtuse angle shown, it's 131. If acute, 41. Given "bottom angle", it's likely supplementary. Let's assume 131.

Problem 6: Isosceles triangle, base angles $23^\circ$ each. Missing angle?
$180 - 23 - 23 = 180 - 46 = 134^\circ$. Option d is $134^\circ$. This matches.

Let's re-evaluate Problem 1. Maybe the text says "Angle A is $25^\circ$ more than"?
If $A = B + 25$:
$(B + 25) + B = 100 \rightarrow 2B = 75 \rightarrow B = 37.5$. Not an option.

Maybe Angle C is not $80$? It looks very much like 80.
Maybe Angle A is $25$ less than Angle C?
If $A = C - 25 = 80 - 25 = 55$.
Then $55 + B + 80 = 180 \rightarrow B + 135 = 180 \rightarrow B = 45$. Not an option.

Let's look at the options for #1 again: a. $59^\circ$, b. $55^\circ$, c. $63^\circ$, d. $54^\circ$.
Is it possible Angle C is $82^\circ$?
$180 - 82 = 98$. $2B - 25 = 98 \rightarrow 2B = 123 \rightarrow 61.5$. No.
Is it possible Angle C is $78^\circ$?
$180 - 78 = 102$. $2B - 25 = 102 \rightarrow 2B = 127 \rightarrow 63.5$. Close to 63.

Let's try working backward from the answers for #1.
If Answer is c. $63^\circ$:
$B = 63$.
$A = 63 - 25 = 38$.
$C = 80$.
Sum = $63 + 38 + 80 = 181$. (Close, maybe rounding error in problem design?)

If Answer is b. $55^\circ$:
$B = 55$.
$A = 55 - 25 = 30$.
$C = 80$.
Sum = $55 + 30 + 80 = 165$. (Way off).

If Answer is a. $59^\circ$:
$B = 59$.
$A = 59 - 25 = 34$.
$C = 80$.
Sum = $59 + 34 + 80 = 173$.

If Answer is d. $54^\circ$:
$B = 54$.
$A = 54 - 25 = 29$.
$C = 80$.
Sum = $54 + 29 + 80 = 163$.

There seems to be a slight inconsistency in Problem 1's text vs standard integer answers, OR I am misreading a number. Let's look at Problem 4, which is similar.
Problem 4: Max needs to cut part of a rectangular piece of fabric. He cuts the corner at a $51^\circ$ angle. What is the angle of the leftover fabric?
A rectangle corner is $90^\circ$. If you cut off a corner with a straight line creating a triangle, the question is ambiguous without a diagram. Usually, "leftover fabric" implies the interior angle of the resulting polygon.
If he cuts a triangle off the corner, the new edge creates two new angles.
However, often these problems ask for the supplementary angle or the other angle in the right triangle formed by the cut.
If it forms a right triangle with the corner, the other acute angle is $90 - 51 = 39^\circ$.
Options: a. $52$, b. $58$, c. $33$, d. $112$. None match 39.
Maybe it asks for the obtuse angle of the remaining shape? $180 - 39 = 141$? No.
Maybe the "cut" angle is relative to the side?
Let's look at the Open Response sheet in the back for clues.
"Max needs to cut part of a rectangular piece of fabric... cuts the corner at a $51^\circ$ angle... what is the angle of the leftover fabric?"
If you cut a corner off a rectangle, you create a pentagon. The two new angles are supplementary to the angles of the removed triangle.
In the removed right triangle, one angle is 90 (the corner), one is 51. The third is $90-51=39$.
The angles on the straight edges of the fabric would be $180 - 51 = 129$ and $180 - 39 = 141$.
None of the multiple choice options ($52, 58, 33, 112$) fit this standard interpretation.

Let's re-read Problem 4 options: a. $52^\circ$, b. $58^\circ$, c. $33^\circ$, d. $112^\circ$.
Is it possible the cut is $57^\circ$? $90-57=33$. Option C is 33. The text looks like 51, but could be 57? Or maybe the angle given is the *other* one?
If the angle of the cut relative to the vertical is 51, the angle relative to horizontal is 39.
Let's assume there might be a typo in my reading or the worksheet. However, Problems 2, 3, and 6 are very clear.

Let's solve the ones that are clearly legible and mathematically sound.

Problem 2:
* Triangle DEF is a right triangle.
* Angle E is the right angle ($90^\circ$).
* Angle F is $16^\circ$.
* Sum of angles = $180^\circ$.
* Angle D = $180^\circ - 90^\circ - 16^\circ$.
* Angle D = $74^\circ$.
* Matches Option c.

Problem 3:
* Two angles are $22^\circ$ and $90^\circ$.
* Missing angle = $180^\circ - 90^\circ - 22^\circ$.
* Missing angle = $68^\circ$.
* Matches Option d.

Problem 6:
* Isosceles triangle.
* Base angles are $23^\circ$ each.
* Sum of base angles = $23^\circ + 23^\circ = 46^\circ$.
* Missing vertex angle = $180^\circ - 46^\circ$.
* Missing angle = $134^\circ$.
* Matches Option d.

Problem 5:
* "A branch in a tree has an angle measured at $49^\circ$."
* "What is the measure of the bottom angle of the branch?"
* This typically refers to supplementary angles on a straight line (the tree trunk).
* Calculation: $180^\circ - 49^\circ = 131^\circ$.
* Matches Option d ($131^\circ$).

Problem 1 (Revisited):
* Text: Angle A is $25^\circ$ less than Angle B. Angle C is $80^\circ$.
* Equation: $(B - 25) + B + 80 = 180$.
* $2B + 55 = 180$.
* $2B = 125$.
* $B = 62.5^\circ$.
* The closest option is c. $63^\circ$. In many school worksheets, if the answer is a decimal like .5, they might round to the nearest whole number for the multiple-choice key, or there is a slight typo in the question numbers (e.g., if Angle C was $79^\circ$, B would be $63^\circ$ exactly: $2B + 54 = 180 \rightarrow 2B=126 \rightarrow B=63$). Given the options, c is the intended answer.

Problem 4 (Revisited):
* Text: Cuts corner at $51^\circ$.
* If we assume the question asks for the other acute angle in the triangle formed by the cut: $90 - 51 = 39$. Not an option.
* If we assume the text actually says $57^\circ$ (which can look like 51 in low res): $90 - 57 = 33$. Option c is $33^\circ$.
* If we assume the text says $38^\circ$: $90 - 38 = 52$. Option a is $52^\circ$.
* Let's look at the shape of the number. It looks like a '5' and a '1'.
* However, looking at the pattern of the other answers being exact integers, and 33 being an option, it is highly probable the angle is meant to result in an integer.
* Let's check if the angle is measured differently. If the cut makes a $51^\circ$ angle with the *long* side, the other angle is 39.
* Let's guess based on common distractors. If the answer were 39, distractors might be nearby.
* Let's look at Option C: $33^\circ$. $90-33=57$. Does the text say 57? The second digit has a flat top and a diagonal down. It looks more like a 1. But a 7 in some fonts has a flat top.
* Let's look at Option A: $52^\circ$. $90-52=38$. Does the text say 38? No, starts with 5.
* Let's look at Option B: $58^\circ$. $90-58=32$.
* Let's look at Option D: $112^\circ$.
* Given the ambiguity, Problem 4 is the hardest to pin down definitively without higher resolution, but c. $33^\circ$ is a strong candidate if the number is actually 57. If the number is strictly 51, none of the answers fit perfectly, but 39 is closest to 33 or 52? No.
* Actually, let's look at the "Open Response" sheet behind it. It has the same problem. "Max needs to cut...". It doesn't give the answer.
* Let's stick to the ones that are mathematically certain.

Final Answer:
Here are the correct choices for the visible multiple-choice questions:

1. c. $63^\circ$ (Calculated value is $62.5^\circ$, rounded to nearest option)
2. c. $74^\circ$
3. d. $68^\circ$
4. c. $33^\circ$ (Assuming the angle is $57^\circ$ due to visual similarity and integer answer requirement; if strictly $51^\circ$, the answer should be $39^\circ$ which is not listed)
5. d. $131^\circ$
6. d. $134^\circ$