Naming Angles Worksheet | PDF Printable Geometry Worksheet - Free Printable

Let's solve this step-by-step. The task is to estimate the size of each angle, identify its type, and write the correct notation (using three letters with the vertex in the middle).

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🔍 Understanding Angle Types:

- Acute angle: Less than 90°
- Right angle: Exactly 90°
- Obtuse angle: Greater than 90° but less than 180°
- Reflex angle: Greater than 180° but less than 360°

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Now let’s go through each angle one by one.

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✔ Example (Given):

- Angle: ∠ABC
- Estimate: 35°
- Type: ACUTE
- Notation: ∠ABC

We’ll follow the same format for the rest.

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1. Angle DEF

- Visual: Small angle at E, between D and F.
- Estimate: ~40°
- Type: ACUTE
- Notation: ∠DEF

✔ *Reasoning*: It's smaller than a right angle, so acute. Looks slightly larger than the example (35°), so ~40°.

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2. Angle GIH

- Visual: Very narrow angle at I, between G and H.
- Estimate: ~20°
- Type: ACUTE
- Notation: ∠GIH

✔ *Reasoning*: Much smaller than the previous one — looks like less than 30°, maybe around 20°.

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3. Angle JKL

- Visual: Wide angle at K, between J and L.
- Estimate: ~120°
- Type: OBTUSE
- Notation: ∠JKL

✔ *Reasoning*: Larger than 90°, but less than 180° — clearly obtuse. Looks about 120°.

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4. Angle NMO

- Visual: Angle at M, appears to be greater than 90°, but not a full straight line.
- Estimate: ~220°
- Type: REFLEX
- Notation: ∠NMO

⚠️ Wait! Let's double-check.

Actually, the angle drawn is the smaller angle at M? But there's a curved arc that goes the long way around — it shows the reflex angle (the larger one). So yes, it's reflex.

But wait — if the arc is large, it means we're measuring the larger angle.

So:
- Estimate: ~220° (since it's more than 180°)
- Type: REFLEX
- Notation: ∠NMO

✔ Yes — reflex angles are those >180°, and the arc indicates which one is being measured.

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5. Angle RPQ

- Visual: A sharp angle at P, between R and Q.
- Estimate: ~70°
- Type: ACUTE
- Notation: ∠RPQ

✔ Looks like a typical acute angle, close to 90° but not quite.

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6. Angle SUT

- Visual: Angle at U, between S and T.
- Estimate: ~100°
- Type: OBTUSE
- Notation: ∠SUT

✔ Slightly wider than 90° — so obtuse.

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7. Angle XWV

- Visual: Right angle symbol at W.
- Estimate: 90°
- Type: RIGHT
- Notation: ∠XWV

✔ The small square indicates a right angle.

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8. Angle ZYA

- Visual: Angle at Z, between Y and A.
- Estimate: ~150°
- Type: OBTUSE
- Notation: ∠ZYA

✔ Clearly greater than 90°, less than 180° — obtuse.

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9. Angle TPE

- Visual: Angle at P, between T and E.
- Estimate: ~200°
- Type: REFLEX
- Notation: ∠TPE

✔ The arc is large, going the long way around. So it's reflex, likely around 200°.

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✔ Final Table:

| Angle | Estimate | Type | Notation |
|-------|----------|----------|----------|
| DEF | 40° | ACUTE | ∠DEF |
| GIH | 20° | ACUTE | ∠GIH |
| JKL | 120° | OBTUSE | ∠JKL |
| NMO | 220° | REFLEX | ∠NMO |
| RPQ | 70° | ACUTE | ∠RPQ |
| SUT | 100° | OBTUSE | ∠SUT |
| XWV | 90° | RIGHT | ∠XWV |
| ZYA | 150° | OBTUSE | ∠ZYA |
| TPE | 200° | REFLEX | ∠TPE |

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📝 Summary of Key Concepts Used:

- Estimation: Compare to known angles (e.g., 90° = right angle).
- Types: Use definitions to classify.
- Notation: Always use three letters with the vertex in the middle.

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✔ All answers are based on visual estimation and standard geometric conventions.

Let me know if you'd like this formatted as a printable table or need help with drawing these angles!