Worksheet on Angles | Questions on Angles | Homework on Angles - Free Printable

The image is a worksheet on measuring angles using a protractor. It shows a semicircular protractor with various rays emanating from the center point O, and labeled points such as P, Q, R, S, T, U.

We are to determine the measure of each angle formed by the rays from point O.

Let’s analyze each ray and measure the angles step-by-step.

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🔍 Step 1: Understand the Protractor

- The protractor has two scales:
- Outer scale: goes from 0° to 180° clockwise (from left to right).
- Inner scale: goes from 0° to 180° counterclockwise (from right to left).

But since all rays originate from O, and we're measuring angles between the horizontal line OP (or OU) and other rays, we can use the standard convention:

- OP is aligned with the 0° mark on the right side.
- OU is aligned with the 0° mark on the left side.
- So, OP → OU forms a straight line = 180°.

We will measure angles from OP or OU depending on direction.

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🔎 Step 2: Identify Each Ray and Measure Angles

Let’s go through each ray from O:

#### ✔ Ray OP
- This is the baseline pointing to the right.
- It aligns with 0° on the right side.
- So, ∠POP = 0°

#### ✔ Ray OQ
- Points toward the upper right.
- On the protractor, it lines up with 150° on the outer scale.
- So, ∠POQ = 150°

> ✔️ But wait — this seems large. Let's double-check.

Actually, looking closely:
- The ray OQ is above the baseline OP.
- On the protractor, if you follow the inner scale (starting from 0° at the right), moving counterclockwise, then:
- OQ points to 30° on the inner scale?

Wait — let's clarify:

In standard protractor usage:
- When you place the center at O, and align the baseline OP with the 0°–180° line, then:
- The angle from OP to OQ is measured counterclockwise (going upward).
- But here, the outer scale increases from 0° at the right to 180° at the left.

So, OP is at 0° (right), and OU is at 180° (left).

Now, look at OQ:
- It points upward and to the right, just past the 40° mark?
- Wait — no, actually, OQ appears to be pointing at 150° on the outer scale?

Wait — that would mean it's going to the left, but OQ is clearly going to the right, so it must be on the lower side.

Let’s re-express this carefully.

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🧩 Correct Interpretation:

The baseline is UP and OP is the horizontal arrow to the right.

The protractor is centered at O, and its straight edge lies along UP, with:
- P at the 0° mark on the right,
- U at the 180° mark on the left.

So, any ray going upward from O will have an angle measured from OP in the counterclockwise direction.

Now, let’s examine each ray:

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🔹 Ray OR:

- Goes straight up.
- This is perpendicular to UP.
- On the protractor, it aligns with 90°.
- So, ∠POR = 90°

✔ Answer: ∠POR = 90°

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🔹 Ray OQ:

- Lies between OR and OP, but below OR? No — wait.

Looking again:
- OQ is above the baseline OP, and to the right of OR? No.

Wait — actually:
- From O, OQ points up and to the right, but less than 90° from OP.
- It lines up with 30° on the outer scale?

Wait — let's read the markings.

Look at the numbers on the protractor:
- On the bottom half, numbers increase from 0° at P (right) to 180° at U (left).
- So, for rays going upward, we use the top arc.

But the scale on the top of the protractor (the curved part) has:
- Outer scale: 0° at P, increasing counterclockwise to 180° at U.
- Inner scale: 0° at U, increasing clockwise to 180° at P.

But typically, when measuring angles from OP, we use the outer scale starting at 0° at P.

So:

#### ✔ Ray OQ:
- It points up and to the right, and intersects the protractor at 30° on the outer scale.
- So, ∠POQ = 30°

✔️ Yes — because from OP (0°) to OQ, moving upward, it hits 30°.

Wait — but visually, OQ looks like it's past 60°?

Let’s check the lines.

From the diagram:
- There is a line from O to Q.
- Looking at the protractor, the markings are:
- At 30°: one line
- At 40°: another
- At 50°: another
- ...
- At 60°: another
- At 70°: another
- At 80°: another
- At 90°: OR

Now, OQ is to the right of OR, meaning less than 90° from OP.

Wait — no! If OR is 90°, then OQ is to the right of OR, which means it's greater than 90°?

Wait — confusion arises from direction.

Let’s fix this:

- OP is to the right (0°)
- OR is straight up (90°)
- OQ is to the right of OR, so beyond 90°?

No — look at the arrows:
- OQ is pointing up and to the right, but not beyond 90° — it’s between 0° and 90°.

Wait — no! The arrow labeled Q is on the right side, above OP, but closer to 90°.

Let’s re-express:

From O, the rays are:

1. OP — to the right → 0°
2. OQ — up and to the right → around 60°?
3. OR — straight up → 90°
4. OS — up and to the left → around 120°
5. OT — further left → around 150°
6. OU — to the left → 180°

Yes — now that makes sense.

So:

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✔ Measuring Each Angle from OP (0°):

We'll measure each angle from OP in the counterclockwise direction.

#### ➤ ∠POQ:
- Ray OQ is at 60° on the outer scale.
- So, ∠POQ = 60°

✔ Answer: 60°

#### ➤ ∠POR:
- Ray OR is at 90°
- So, ∠POR = 90°

✔ Answer: 90°

#### ➤ ∠POS:
- Ray OS is above and to the left of OR
- It aligns with 120° on the outer scale.
- So, ∠POS = 120°

✔ Answer: 120°

#### ➤ ∠POT:
- Ray OT is even further left, at 150°
- So, ∠POT = 150°

✔ Answer: 150°

#### ➤ ∠POU:
- Ray OU is directly to the left → 180°
- So, ∠POU = 180°

✔ Answer: 180°

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🔹 Additional Angles (if asked):

You might also be asked for angles like:

#### ➤ ∠ROQ:
- From OR (90°) to OQ (60°) → but that’s backwards.
- Actually, OQ is at 60°, OR at 90°, so angle between them is:
- ∠QOR = |90° – 60°| = 30°

✔ Answer: 30°

#### ➤ ∠ROS:
- OR = 90°, OS = 120°
- So, ∠ROS = 120° – 90° = 30°

✔ Answer: 30°

#### ➤ ∠SOT:
- OS = 120°, OT = 150°
- So, ∠SOT = 150° – 120° = 30°

✔ Answer: 30°

#### ➤ ∠TOU:
- OT = 150°, OU = 180°
- So, ∠TOU = 180° – 150° = 30°

✔ Answer: 30°

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📌 Summary of Key Angles:

| Angle | Measure |
|-------------|---------|
| ∠POQ | 60° |
| ∠POR | 90° |
| ∠POS | 120° |
| ∠POT | 150° |
| ∠POU | 180° |
| ∠QOR | 30° |
| ∠ROS | 30° |
| ∠SOT | 30° |
| ∠TOU | 30° |

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✔ Final Answer:

If the task is to measure the angles shown, then:

- ∠POQ = 60°
- ∠POR = 90°
- ∠POS = 120°
- ∠POT = 150°
- ∠POU = 180°

And the angles between adjacent rays are all 30°, suggesting a regular division.

This worksheet is designed to help students practice reading a protractor accurately.

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📝 How to Use the Protractor:

1. Place the center of the protractor at point O.
2. Align the baseline with OP (the horizontal line).
3. Read the angle where the ray crosses the protractor scale.
4. Use the outer scale for angles measured from OP going upward (counterclockwise).

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✔ Conclusion: The angles are measured as follows:
- OQ: 60°
- OR: 90°
- OS: 120°
- OT: 150°
- OU: 180°

All measurements are based on the outer scale of the protractor, starting from OP (0°).

Let me know if you'd like a printable version or need to find specific angles!