Measuring Angles with a Protractor Worksheet - Free Printable

Let’s go through each angle one by one. We’ll check if the drawn ray matches the given angle and whether the label (acute, obtuse, or right) is correct.

Remember:
- Acute angle = less than 90°
- Right angle = exactly 90°
- Obtuse angle = more than 90° but less than 180°

We are told to draw a second ray to create the shown angle — but in this answer key, the rays are already drawn. So we just need to verify that each drawing matches the labeled degree and type.

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Top Left: 35° — labeled “acute”

→ The protractor shows a ray going from 0° to 35°. That’s correct.
→ 35° < 90° → acute → correct label.

✔ Correct.

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Top Right: 175° — labeled “obtuse”

→ Ray goes from 0° to 175° on the protractor.
→ 175° > 90° and < 180° → obtuse → correct label.

✔ Correct.

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Middle Left: 105° — labeled “obtuse”

→ Ray points to 105° on the protractor.
→ 105° > 90° → obtuse → correct.

✔ Correct.

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Middle Right: 55° — labeled “acute”

→ Ray at 55° → less than 90° → acute → correct.

✔ Correct.

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Bottom Left: 65° — labeled “acute”

Wait — here’s a problem!

The worksheet says 65°, and labels it “acute” — which is correct because 65° < 90°.

BUT — look at the drawing: the ray is pointing to 115°, not 65°!

On a standard protractor, if you start from the left (0°), then:

- Going clockwise, 65° would be near the top-left side.
- But the ray here is going to the right side — that’s 115° (because 180° - 65° = 115°).

So either:
- The angle should be labeled 115°, OR
- The ray should be drawn to 65° (on the other side).

But since the label says “65°” and “acute”, and the drawing shows 115°, there’s a mismatch.

However — wait! Let’s double-check how the protractor is being used.

In some worksheets, they might measure from the right side as 0°. But looking at all other problems, they’re measuring from the LEFT side (starting at 0° on the left).

For example:
- 35°: ray starts at left 0°, goes up to 35° → correct.
- 175°: starts at left 0°, goes almost flat to the right → 175° → correct.
- 105°: starts at left 0°, goes up to 105° → correct.
- 55°: same → correct.
- 95°: starts at left 0°, goes to 95° → correct.
- 115°: starts at left 0°, goes to 115° → correct.
- 145°: starts at left 0°, goes to 145° → correct.

Now for the 65° box: the ray is drawn to where? If you follow the arc from the left 0°, the ray hits 115°, not 65°.

So this is an error in the answer key.

But hold on — maybe the student was supposed to draw the ray themselves? The instruction says: “Draw a second ray to create the angle shown.” And “The first one is done for you.”

Looking back at the top-left (35°), it’s marked as “done for you”. So perhaps the rest are meant to be filled in by the student — but in this image, they’re all filled in as part of the “Answer Key”.

That means — in the official answer key, the 65° box has a mistake.

Actually — let me re-express:

If the angle is supposed to be 65°, and you start from the left baseline (0°), then the ray should point to 65° — which is between 60° and 70°, closer to 60°.

But in the image, the ray is pointing to 115° — which is between 110° and 120°.

So unless the protractor is flipped, this is wrong.

Alternatively — maybe they’re measuring from the right?

Check the 175°: if you measure from the right, 175° would be almost at the left end — which matches the drawing (ray nearly flat to the left). Wait — no, in the 175° box, the ray is going to the far right — which from the left 0° is 175°, from the right 0° would be 5°.

This is confusing.

Let’s use a consistent method:

Standard protractor usage in schools:
- Place the center hole on the vertex.
- Align the baseline with one ray (usually the horizontal one going left).
- Read the angle where the second ray crosses the scale.

In ALL boxes except the 65° one, the horizontal ray is aligned to the LEFT 0°, and the second ray is read accordingly.

In the 65° box, the second ray is at 115° — so if the intended angle is 65°, this is incorrect.

But wait — what if the angle is measured from the OTHER side? Sometimes angles can be measured clockwise or counterclockwise.

Actually — 65° and 115° are supplementary (add to 180°). So if you have a straight line, and you draw a ray making 65° on one side, it makes 115° on the other.

But the problem says: “create the angle shown” — meaning the smaller angle? Or the one indicated?

Looking at the labeling:

In the 35° box, they show the small angle (35°), not the big one (145°).

Similarly, 55° — small angle.

105° — that’s already obtuse, so they show the larger one.

So for 65°, they should show the 65° angle, not the 115°.

Therefore, the drawing in the 65° box is WRONG — it should be drawn to 65°, not 115°.

But since this is an ANSWER KEY, and it's labeled as such, perhaps it's a typo in the key.

Alternatively — maybe I misread.

Let me look again at the 65° box:

The horizontal ray is on the left. The second ray is going up and to the right — crossing the protractor at approximately 115° mark.

Yes — definitely 115°.

But the label says 65° and “acute”.

115° is obtuse, not acute.

So two errors:
1. The angle drawn is 115°, not 65°.
2. It’s labeled “acute”, but 115° is obtuse.

Whereas 65° is acute — so the label “acute” is correct for 65°, but the drawing doesn’t match.

Conclusion: This box contains an error in the answer key.

But wait — let’s check the bottom middle: 115° — labeled “obtuse”

There, the ray is drawn to 115° — correct.

And bottom right: 145° — drawn to 145° — correct.

So why is the 65° box showing 115°?

Possibility: Maybe the student was supposed to draw the reflex angle or something? No, the instructions say “create the angle shown” — and 65° is shown.

Another possibility: In some curricula, they teach to always measure from the left, but sometimes students get confused.

Given that this is an answer key, and all others are correct, likely this is a printing error.

But for the purpose of this exercise — since the user asked to solve the problem accurately, and this is presented as an answer key, I must report what is correct.

Actually — rereading the original instruction:

“Draw a second ray to create the angle shown. Label each angle as right, acute, or obtuse. The first one is done for you.”

So for each box, the angle measure is given (e.g., 35°), and the student must draw the ray and label the type.

In the answer key, they’ve provided the completed version.

For the 65° box, they drew the ray at 115° and labeled it “acute” — which is inconsistent.

Because:
- If the angle is 65°, ray should be at 65°, label “acute” — correct.
- If the ray is at 115°, angle is 115°, label should be “obtuse”.

They have mixed them.

So in reality, for the 65° problem, the correct drawing should have the ray at 65°, and label “acute”.

But in this image, it’s incorrectly drawn at 115° and still labeled “acute” — which is wrong because 115° is not acute.

Therefore, this entry in the answer key is flawed.

However, since the task is to "solve the problem accurately", and assuming we are to evaluate or complete the worksheet correctly, I will provide the correct versions.

But the user didn't ask to correct the key — they uploaded an image containing a task, and said "solve the problem accurately".

Looking back: the image is titled "Protractor Worksheets" and "ANSWER KEY", so it's presenting solutions.

Perhaps the user wants us to verify or explain.

But according to the rules, I need to solve the problem.

Maybe the "problem" is to understand how to do these, and the image is reference.

To clarify: I think the best approach is to assume that for each given angle, we confirm if the drawing and label are correct, and if not, state the correction.

Since this is an answer key, and most are correct except one, I'll note that.

But for the final answer, since the user might expect the correct completions, I'll list what each should be.

Let me make a table:

| Given Angle | Correct Drawing Position | Correct Label | What's Shown in Image | Verdict |
|-------------|--------------------------|---------------|------------------------|---------|
| 35° | 35° from left | acute | 35°, acute | ✔ |
| 175° | 175° from left | obtuse | 175°, obtuse | ✔ |
| 105° | 105° from left | obtuse | 105°, obtuse | ✔ |
| 55° | 55° from left | acute | 55°, acute | ✔ |
| 65° | 65° from left | acute | 115°, acute | ✘ Should be 65° and acute; currently shows 115° which is obtuse |
| 95° | 95° from left | obtuse | 95°, obtuse | ✔ |
| 115° | 115° from left | obtuse | 115°, obtuse | ✔ |
| 145° | 145° from left | obtuse | 145°, obtuse | ✔ |

So only the 65° box is incorrect in the answer key.

Therefore, for accuracy, the 65° angle should have the ray drawn at 65 degrees (not 115), and labeled "acute".

All others are correct.

Final Answer: All angles are correctly drawn and labeled except for the 65° angle, which should be drawn at 65° (not 115°) and is correctly labeled as acute. The current drawing for 65° shows 115°, which is obtuse, so it is inconsistent. For accuracy, redraw the ray for 65° to point to 65° on the protractor.