Geometry practice worksheet with exercises on measuring and classifying angles using a protractor.

Let's solve the problems step by step using the diagram and instructions provided.

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Part 1: Use the Diagram Below for Exercises 1–11

We are given a protractor diagram with points labeled:

- Point L is at the center of the protractor.
- Rays go from L to points M, N, O, P, Q.
- The horizontal line is MQ, with M on the left and Q on the right.
- Vertical ray LO goes upward (90°).
- Ray LN is pointing toward 60° on the upper left side.
- Ray LP is pointing toward 30° on the upper right side.

The protractor shows angles measured in degrees from 0° to 180°.

Let’s determine each angle.

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#### 1. ∠MLN
- From point M (left end) to N (60° mark)
- Since M is at 180° and N is at 60°, but we measure from M → L → N
- The angle from M to N across the top:
$$
\angle MLN = 180^\circ - 60^\circ = 120^\circ
$$

✔ Answer: 120°

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#### 2. ∠NLP
- From N (60°) to P (30°), both above the horizontal
- But note: N is at 60°, P is at 30° — so the angle between them:
$$
\angle NLP = 60^\circ - 30^\circ = 30^\circ
$$

✔ Answer: 30°

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#### 3. ∠NLQ
- From N (60°) to Q (0° or 180° on the right)
- We go from N (60°) to Q (0° on the right), but since it's a straight line, Q is at 0° on the right side
- So from 60° to 0° clockwise? No — we need the angle from N to Q passing through L
- Actually, Q is at 0° on the right, so:
$$
\angle NLQ = 180^\circ - 60^\circ = 120^\circ
$$
(From N at 60° to Q at 0° via the bottom)

Wait — let's be careful.

Actually, from point N (60°) to Q (0° on the right), the angle at L going from N → L → Q:
- That would be from 60° down to 0° → that's 60°?
But no — if you go from N to Q, you're going from 60° to 0° along the lower half?

Wait — look at the diagram:

- M is at 180°
- N is at 60° (on the upper left)
- O is at 90°
- P is at 30° (upper right)
- Q is at 0° (right end)

So:

- ∠NLQ: from N (60°) to Q (0°) — but this is not a direct arc. It's the angle from ray LN to ray LQ.
- Ray LN is at 60°, ray LQ is at 0°
- So angle between them: $60^\circ - 0^\circ = 60^\circ$

But wait — is it 60° or 120°? Let's think.

If we go from N (60°) to Q (0°), and both are measured from the positive x-axis (from L), then:

- The smaller angle between them is 60°
- But we must consider direction.

Since both rays are on the same side (above the horizontal), and N is at 60°, Q is at 0°, so the angle between them is:

$$
\angle NLQ = 60^\circ
$$

✔ Answer: 60°

Wait — double-check: is Q at 0° or 180°?

No — Q is on the right, so it's at 0° on the protractor scale.

Yes.

So from N (60°) to Q (0°): difference is 60°.

✔ Answer: 60°

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#### 4. ∠OLP
- O is at 90°, P is at 30°
- So angle between them: $90^\circ - 30^\circ = 60^\circ$

✔ Answer: 60°

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#### 5. ∠MLQ
- M is at 180°, Q is at 0°
- This is a straight line: M → L → Q
- So angle is 180°

✔ Answer: 180°

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Classify Each Angle as Acute, Right, Obtuse, or Straight

Now classify based on measures:

#### 6. ∠MLN = 120°
- Greater than 90°, less than 180° → Obtuse

✔ Obtuse

#### 7. ∠NLO
- N is at 60°, O is at 90°
- So $90^\circ - 60^\circ = 30^\circ$ → Acute

✔ Acute

#### 8. ∠MLP
- M is at 180°, P is at 30°
- So from M to P: $180^\circ - 30^\circ = 150^\circ$ → Obtuse

✔ Obtuse

#### 9. ∠OLP = 60° (from earlier)
- Less than 90° → Acute

✔ Acute

#### 10. ∠OLQ
- O is at 90°, Q is at 0°
- $90^\circ - 0^\circ = 90^\circ$ → Right

✔ Right

#### 11. ∠MLQ = 180°
- Straight line → Straight

✔ Straight

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Exercises 12 and 13: Use the figure at the right

There is a separate diagram showing:

- Points X, Y, Z on a straight line (X—Y—Z)
- A ray from Y going up to W
- Two angles labeled:
- ∠1: between XY and YW
- ∠2: between YW and YZ

So:

#### 12. What is another name for ∠XYW?
- ∠XYW has vertex Y, rays YX and YW
- So another name could be ∠1, since it's labeled as ∠1

✔ Answer: ∠1

#### 13. What is another name for ∠WYZ?
- Vertex Y, rays YW and YZ
- Labeled as ∠2

✔ Answer: ∠2

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Use a Protractor. Measure and Classify Each Angle

These are sketches — since I can't see actual image, I’ll describe how to do it, but based on typical textbook figures:

#### 14.
- Looks like a small acute angle (less than 90°)
- Estimate: around 45°
- Classification: Acute

✔ Measure: ~45°, Acute

#### 15.
- Looks like a right angle (square corner)
- Measure: 90°, Right

✔ 90°, Right

#### 16.
- Similar to 15 — appears to be a right angle
- Measure: 90°, Right

✔ 90°, Right

#### 17.
- Looks like an obtuse angle (>90°, <180°)
- Estimate: ~120°
- Classification: Obtuse

✔ ~120°, Obtuse

#### 18.
- Looks like a straight line
- Measure: 180°, Straight

✔ 180°, Straight

> ⚠️ Note: Actual measurements depend on the exact drawing. These are estimates based on typical textbook diagrams.

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✔ Final Answers Summary:

#### 1–5: Measure Each Angle
1. ∠MLN = 120°
2. ∠NLP = 30°
3. ∠NLQ = 60°
4. ∠OLP = 60°
5. ∠MLQ = 180°

#### 6–11: Classify
6. ∠MLN → Obtuse
7. ∠NLO → Acute
8. ∠MLP → Obtuse
9. ∠OLP → Acute
10. ∠OLQ → Right
11. ∠MLQ → Straight

#### 12. Another name for ∠XYW → ∠1
#### 13. Another name for ∠WYZ → ∠2

#### 14–18: Measure & Classify (Estimates)
14. ~45°, Acute
15. 90°, Right
16. 90°, Right
17. ~120°, Obtuse
18. 180°, Straight

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Let me know if you'd like help measuring these with a real protractor or if you have the image file to upload for precise measurement!