Angles Worksheets | Free - CommonCoreSheets - Free Printable

Let’s go through each angle one by one. We’ll use the protractor shown in each diagram to find the measure of the angle.

Remember:
- The protractor has two scales — inner and outer.
- Always start from 0° on the side where the angle begins (the ray that lines up with the bottom edge).
- Read the number where the other ray crosses the curved edge.

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1) The angle starts at 0° on the right, and the other ray points to 85°.
→ Angle = 85°

2) Starts at 0° on the left, other ray points to 90°.
→ Angle = 90°

3) Starts at 0° on the left, other ray points to 15°.
→ Angle = 15°

4) Starts at 0° on the right, other ray points to 50°.
→ Angle = 50°

5) Starts at 0° on the right, other ray points to 10°.
→ Angle = 10°

6) Starts at 0° on the left, other ray points to 80°.
→ Angle = 80°

7) Starts at 0° on the left, other ray points to 30°.
→ Angle = 30°

8) Starts at 0° on the left, other ray points to 45°.
→ Angle = 45°

9) Starts at 0° on the right, other ray points to 160°? Wait — let’s check again.

Actually, for #9: The angle opens to the left. The ray is pointing to 20° on the *inner* scale? No — look carefully.

The base ray is on the right (0°), and the top ray goes to the left side. On the protractor, when you start from the right, the numbers go clockwise. So if the ray is near the left end, it’s around 160°? But wait — actually, looking at the diagram, the angle is small — it’s only 20° from the left side? Let me reorient.

Better way: In #9, the vertex is on the right, one ray goes left along the baseline, the other ray goes up-left. That means we’re measuring from the left side as 0°. So read the inner scale: the ray hits 20°.

Wait — no! Actually, in standard protractor use:

If the angle opens to the left, you use the inner scale starting from 0° on the left.

In #9: One ray is along the bottom going left (so 0° on left), the other ray is going up-left — it crosses at 20° on the inner scale.

But wait — looking again: the ray is very close to the bottom — it’s only a little above horizontal. So yes, 20°.

Actually, let me double-check all using consistent method:

For any angle:
- Place protractor so center is on vertex.
- Align one ray with 0° line.
- Read where the other ray hits the arc.

In #9: The ray that’s not on the baseline is pointing to 20° on the *inner* scale (since we started from left 0°).

So → 20°

10) Starts at 0° on the left, other ray points to 70°.
→ Angle = 70°

Wait — let me verify #9 again because sometimes these can be tricky.

Looking at #9: The angle is between the left-pointing ray and a ray going slightly upward to the left. So if we set 0° on the left, then the moving ray is at 20°. Yes.

Alternatively, if someone mistakenly reads from the right, they might say 160°, but that would be the reflex angle — we always take the smaller angle unless told otherwise. All angles here are acute or right or obtuse under 180°, and clearly less than 90° except some.

Actually, #9 looks like about 20° — yes.

Now let’s list them cleanly:

1) 85°
2) 90°
3) 15°
4) 50°
5) 10°
6) 80°
7) 30°
8) 45°
9) 20°
10) 70°

I think that’s correct.

Final Answer:
1. 85°
2. 90°
3. 15°
4. 50°
5. 10°
6. 80°
7. 30°
8. 45°
9. 20°
10. 70°