Angles measurement worksheet - Free Printable
Educational worksheet: Angles measurement worksheet. Download and print for classroom or home learning activities.
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Step-by-step solution for: Angles measurement worksheet
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Show Answer Key & Explanations
Step-by-step solution for: Angles measurement worksheet
Let’s go through each angle one by one. We’ll read the protractor carefully — remember, we always start from 0° on the side where the blue line is pointing along the bottom (the baseline). Then we follow the other blue line up to see what number it points to on the curved scale.
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1) The bottom line goes to the right → so we use the inner scale (starts at 0 on the right). The top line points to 95°.
✔ Answer: 95°
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2) Bottom line goes to the left → use outer scale (starts at 0 on the left). Top line points straight up → that’s 90°.
✔ Answer: 90°
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3) Bottom line goes to the left → use outer scale. The slanted line points to 170°? Wait — let’s check again. From left 0°, going clockwise, the line is just before 180° — actually, it’s at 170°? No — wait! Look closely: the line is between 160 and 180, but closer to 170? Actually, no — in this case, since the angle opens to the right, maybe we should measure from the right? Let me re-think.
Actually, standard rule: if the baseline is on the left, read the outer numbers. If on the right, read the inner numbers.
In #3: baseline arrow is pointing LEFT → so we read the OUTER scale (which starts at 0 on the left). The other arm is pointing near 170? But looking at the image — the angle is very small? Wait — no! The two lines form a wide angle — almost flat. So yes, from left 0°, going around to the other line — it hits 170°? Actually, let’s count: from 0 on left, 10, 20... up to 170 — yes, the line is exactly on 170.
Wait — correction! In many protractors, when the baseline is on the left, you read the outer ring. The second line is pointing to 170 on the outer ring? Actually, looking again — the line is pointing to 170° on the outer scale? Or is it 10°? No — because the angle is obtuse (wide), not acute.
Actually — I think I made a mistake. Let’s look at the direction of the arrows.
In #3: one arrow points left (baseline), the other points slightly upward to the right. That means the angle measured from the left baseline going counterclockwise would be large — but protractors usually measure the smaller angle unless specified.
Wait — no, in these diagrams, they are showing the actual angle formed by the two rays. Since one ray is pointing left and the other is pointing slightly up-right, the angle between them is actually 170°, because from left (180°) down to the slight incline — no.
Better way: place your eye at the center. One ray goes to 180° (left), the other goes to about 10° on the inner scale? That would make the angle 170° (because 180 - 10 = 170). Yes!
So: if one side is at 180° (left) and the other is at 10° (on the inner scale, which is for right-side baseline), then the angle between them is 170°.
But to avoid confusion — let’s use this trick:
> Always align the protractor so that one side of the angle is on 0°. Then read where the other side lands.
In #3: if we consider the left-pointing ray as our “zero”, then we need to read the outer scale starting from 0 on the left. Moving clockwise, the other ray lands at 170°? Actually, no — moving clockwise from left 0°, you hit 10, 20, ..., 170, 180. The ray is pointing to about 10° past 160? Wait — looking at the image again (mentally), the ray is very close to the horizontal right, so from left 0°, going all the way around almost to 180° — so yes, 170°.
Actually, let’s double-check with another method: the angle looks like it’s 10° above the horizontal right. So if the left ray is 180°, and the right-up ray is 10°, then the difference is 170°. Correct.
✔ Answer: 170°
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4) Baseline points right → use inner scale. Other line points to 50°.
✔ Answer: 50°
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5) Baseline points right → inner scale. Other line is very low — only 10° above baseline.
✔ Answer: 10°
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6) Baseline points left → outer scale. Other line points to 80° on the outer scale? Let’s see: from left 0°, going clockwise, the line is at 80°? Actually, looking — it’s between 70 and 90, closer to 80. Yes, 80°.
Wait — no! If baseline is on left, and we’re measuring the angle opening to the right, then from left 0°, moving clockwise to the line — it should be 80°? But visually, the angle looks like 80° from the left? Actually, no — if the line is going up to the right, and baseline is left, then the angle is 100°? I’m getting confused.
Let me reset.
Standard approach:
- Place protractor so that the vertex is at the center.
- Align one side of the angle with the 0° mark.
- Read the degree where the other side crosses the scale.
In #6: one side is pointing left → so we can treat that as 180° if using inner scale, or 0° if using outer scale.
If we use outer scale (0 on left), then the other side is pointing to 80°? But that would mean the angle is 80°, which seems too small — because the line is steep.
Actually, looking at the diagram: the line is going up to the right, making an acute angle with the horizontal right. But since the baseline is drawn to the left, the angle shown is the reflex? No — in these worksheets, they always show the smaller angle unless it's clearly obtuse.
Wait — in #6, the two lines form an angle that is less than 90°? No — from left to up-right, it’s more than 90°.
Let’s calculate: if the right-horizontal is 0°, then left is 180°, and the up-right line is at, say, 80° from right? Then from left (180°) to that line is 100° (because 180 - 80 = 100).
Yes! So the angle is 100°.
How to read on protractor: if baseline is on left, and you want the angle inside, you read the outer scale from 0 on left to the line — which should be 100°? Let’s see: outer scale from left 0°: 0, 10, 20, ..., 90 (top), 100, etc. The line is at 100° on the outer scale? In the image, it looks like it’s at 80° on the inner scale, which corresponds to 100° on the outer scale.
Yes — so answer is 100°.
✔ Answer: 100°
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7) Baseline points left → outer scale. Other line points to 30° on the outer scale? From left 0°, moving clockwise, the line is at 30°? But that would be a small angle — visually, it’s about 30° above the horizontal right, so from left, it’s 150°?
Again: if right-horizontal is 0°, left is 180°, and the line is at 30° from right, then angle from left is 150°.
On protractor: if baseline is left (outer scale 0°), then the line is at 150° on the outer scale? Let’s check: outer scale from left: 0, 10, 20, ..., 150 — yes, the line is at 150°.
✔ Answer: 150°
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8) Baseline points left → outer scale. Other line points to 45°? From left 0°, the line is at 45° on the outer scale? But visually, it’s halfway between 0 and 90 on the left side — so 45°? But that would be acute, while the angle shown is obtuse.
No — if baseline is left, and the line is going up-left, then the angle between them is 45°? But in the diagram, the line is going up to the left, so from left baseline, rotating up to that line — it’s 45°? But that doesn’t match the visual.
Actually, in #8, the baseline is pointing left, and the other line is pointing up-left, forming a 45° angle with the baseline? But typically, we measure the smaller angle.
Looking at the protractor: if we use outer scale (0 on left), the line is at 45°? But in the image, it’s labeled as 45° on the inner scale? I think I need to trust the scale.
Upon careful thought: in #8, the angle is between the left-pointing ray and the up-left ray. On the protractor, if we set 0 on left, the other ray is at 45° on the outer scale? But that would be correct for a 45° angle.
However, in many such diagrams, when the ray is in the second quadrant, they might expect the measurement from the positive x-axis.
To resolve: let’s assume that for consistency, we always measure the angle from the baseline ray to the other ray in the direction that gives the smaller angle, but in these cases, they are showing the actual angle formed.
In #8, the two rays form a 45° angle? Or 135°? Visually, it looks like 45° from the vertical or something.
Let’s use coordinates: suppose the vertex is origin. Left ray is 180°, up-left ray is 135° (since 90 + 45 = 135). So the angle between 180° and 135° is 45°.
Yes! So the angle is 45°.
On protractor: if baseline is at 180° (left), and other ray at 135°, then the difference is 45°. When reading, if we have baseline on left, and we read the outer scale, the other ray should be at 45° on the outer scale? Outer scale from left 0°: 0 at left, 90 at top, 180 at right. So 135° from positive x-axis is 45° from negative x-axis, which on outer scale would be 45°.
Yes.
✔ Answer: 45°
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Now let’s list all answers clearly:
1) 95°
2) 90°
3) 170°
4) 50°
5) 10°
6) 100°
7) 150°
8) 45°
I think that’s correct. Let me quickly verify #3 and #6 again.
For #3: baseline left, other ray almost right — so angle is nearly 180°, specifically 170° — yes.
For #6: baseline left, other ray up-right — so from left, turning to up-right, it’s 100° (since 90° would be straight up, and this is a bit past that? No — if it’s 80° from right, then from left it’s 100° — yes.
All good.
Final Answer:
1) 95°
2) 90°
3) 170°
4) 50°
5) 10°
6) 100°
7) 150°
8) 45°
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1) The bottom line goes to the right → so we use the inner scale (starts at 0 on the right). The top line points to 95°.
✔ Answer: 95°
---
2) Bottom line goes to the left → use outer scale (starts at 0 on the left). Top line points straight up → that’s 90°.
✔ Answer: 90°
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3) Bottom line goes to the left → use outer scale. The slanted line points to 170°? Wait — let’s check again. From left 0°, going clockwise, the line is just before 180° — actually, it’s at 170°? No — wait! Look closely: the line is between 160 and 180, but closer to 170? Actually, no — in this case, since the angle opens to the right, maybe we should measure from the right? Let me re-think.
Actually, standard rule: if the baseline is on the left, read the outer numbers. If on the right, read the inner numbers.
In #3: baseline arrow is pointing LEFT → so we read the OUTER scale (which starts at 0 on the left). The other arm is pointing near 170? But looking at the image — the angle is very small? Wait — no! The two lines form a wide angle — almost flat. So yes, from left 0°, going around to the other line — it hits 170°? Actually, let’s count: from 0 on left, 10, 20... up to 170 — yes, the line is exactly on 170.
Wait — correction! In many protractors, when the baseline is on the left, you read the outer ring. The second line is pointing to 170 on the outer ring? Actually, looking again — the line is pointing to 170° on the outer scale? Or is it 10°? No — because the angle is obtuse (wide), not acute.
Actually — I think I made a mistake. Let’s look at the direction of the arrows.
In #3: one arrow points left (baseline), the other points slightly upward to the right. That means the angle measured from the left baseline going counterclockwise would be large — but protractors usually measure the smaller angle unless specified.
Wait — no, in these diagrams, they are showing the actual angle formed by the two rays. Since one ray is pointing left and the other is pointing slightly up-right, the angle between them is actually 170°, because from left (180°) down to the slight incline — no.
Better way: place your eye at the center. One ray goes to 180° (left), the other goes to about 10° on the inner scale? That would make the angle 170° (because 180 - 10 = 170). Yes!
So: if one side is at 180° (left) and the other is at 10° (on the inner scale, which is for right-side baseline), then the angle between them is 170°.
But to avoid confusion — let’s use this trick:
> Always align the protractor so that one side of the angle is on 0°. Then read where the other side lands.
In #3: if we consider the left-pointing ray as our “zero”, then we need to read the outer scale starting from 0 on the left. Moving clockwise, the other ray lands at 170°? Actually, no — moving clockwise from left 0°, you hit 10, 20, ..., 170, 180. The ray is pointing to about 10° past 160? Wait — looking at the image again (mentally), the ray is very close to the horizontal right, so from left 0°, going all the way around almost to 180° — so yes, 170°.
Actually, let’s double-check with another method: the angle looks like it’s 10° above the horizontal right. So if the left ray is 180°, and the right-up ray is 10°, then the difference is 170°. Correct.
✔ Answer: 170°
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4) Baseline points right → use inner scale. Other line points to 50°.
✔ Answer: 50°
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5) Baseline points right → inner scale. Other line is very low — only 10° above baseline.
✔ Answer: 10°
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6) Baseline points left → outer scale. Other line points to 80° on the outer scale? Let’s see: from left 0°, going clockwise, the line is at 80°? Actually, looking — it’s between 70 and 90, closer to 80. Yes, 80°.
Wait — no! If baseline is on left, and we’re measuring the angle opening to the right, then from left 0°, moving clockwise to the line — it should be 80°? But visually, the angle looks like 80° from the left? Actually, no — if the line is going up to the right, and baseline is left, then the angle is 100°? I’m getting confused.
Let me reset.
Standard approach:
- Place protractor so that the vertex is at the center.
- Align one side of the angle with the 0° mark.
- Read the degree where the other side crosses the scale.
In #6: one side is pointing left → so we can treat that as 180° if using inner scale, or 0° if using outer scale.
If we use outer scale (0 on left), then the other side is pointing to 80°? But that would mean the angle is 80°, which seems too small — because the line is steep.
Actually, looking at the diagram: the line is going up to the right, making an acute angle with the horizontal right. But since the baseline is drawn to the left, the angle shown is the reflex? No — in these worksheets, they always show the smaller angle unless it's clearly obtuse.
Wait — in #6, the two lines form an angle that is less than 90°? No — from left to up-right, it’s more than 90°.
Let’s calculate: if the right-horizontal is 0°, then left is 180°, and the up-right line is at, say, 80° from right? Then from left (180°) to that line is 100° (because 180 - 80 = 100).
Yes! So the angle is 100°.
How to read on protractor: if baseline is on left, and you want the angle inside, you read the outer scale from 0 on left to the line — which should be 100°? Let’s see: outer scale from left 0°: 0, 10, 20, ..., 90 (top), 100, etc. The line is at 100° on the outer scale? In the image, it looks like it’s at 80° on the inner scale, which corresponds to 100° on the outer scale.
Yes — so answer is 100°.
✔ Answer: 100°
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7) Baseline points left → outer scale. Other line points to 30° on the outer scale? From left 0°, moving clockwise, the line is at 30°? But that would be a small angle — visually, it’s about 30° above the horizontal right, so from left, it’s 150°?
Again: if right-horizontal is 0°, left is 180°, and the line is at 30° from right, then angle from left is 150°.
On protractor: if baseline is left (outer scale 0°), then the line is at 150° on the outer scale? Let’s check: outer scale from left: 0, 10, 20, ..., 150 — yes, the line is at 150°.
✔ Answer: 150°
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8) Baseline points left → outer scale. Other line points to 45°? From left 0°, the line is at 45° on the outer scale? But visually, it’s halfway between 0 and 90 on the left side — so 45°? But that would be acute, while the angle shown is obtuse.
No — if baseline is left, and the line is going up-left, then the angle between them is 45°? But in the diagram, the line is going up to the left, so from left baseline, rotating up to that line — it’s 45°? But that doesn’t match the visual.
Actually, in #8, the baseline is pointing left, and the other line is pointing up-left, forming a 45° angle with the baseline? But typically, we measure the smaller angle.
Looking at the protractor: if we use outer scale (0 on left), the line is at 45°? But in the image, it’s labeled as 45° on the inner scale? I think I need to trust the scale.
Upon careful thought: in #8, the angle is between the left-pointing ray and the up-left ray. On the protractor, if we set 0 on left, the other ray is at 45° on the outer scale? But that would be correct for a 45° angle.
However, in many such diagrams, when the ray is in the second quadrant, they might expect the measurement from the positive x-axis.
To resolve: let’s assume that for consistency, we always measure the angle from the baseline ray to the other ray in the direction that gives the smaller angle, but in these cases, they are showing the actual angle formed.
In #8, the two rays form a 45° angle? Or 135°? Visually, it looks like 45° from the vertical or something.
Let’s use coordinates: suppose the vertex is origin. Left ray is 180°, up-left ray is 135° (since 90 + 45 = 135). So the angle between 180° and 135° is 45°.
Yes! So the angle is 45°.
On protractor: if baseline is at 180° (left), and other ray at 135°, then the difference is 45°. When reading, if we have baseline on left, and we read the outer scale, the other ray should be at 45° on the outer scale? Outer scale from left 0°: 0 at left, 90 at top, 180 at right. So 135° from positive x-axis is 45° from negative x-axis, which on outer scale would be 45°.
Yes.
✔ Answer: 45°
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Now let’s list all answers clearly:
1) 95°
2) 90°
3) 170°
4) 50°
5) 10°
6) 100°
7) 150°
8) 45°
I think that’s correct. Let me quickly verify #3 and #6 again.
For #3: baseline left, other ray almost right — so angle is nearly 180°, specifically 170° — yes.
For #6: baseline left, other ray up-right — so from left, turning to up-right, it’s 100° (since 90° would be straight up, and this is a bit past that? No — if it’s 80° from right, then from left it’s 100° — yes.
All good.
Final Answer:
1) 95°
2) 90°
3) 170°
4) 50°
5) 10°
6) 100°
7) 150°
8) 45°
Parent Tip: Review the logic above to help your child master the concept of measuring angle worksheet.
