FREE Printable Types Of Angles Worksheets [PDFs] Brighterly - Free Printable

Absolutely! Let’s solve the worksheet “Identifying the Types of Angles” by analyzing each clock and determining the type of angle formed by the hour and minute hands.

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📌 Types of Angles to Remember:

- Acute Angle: Less than 90°
- Right Angle: Exactly 90°
- Obtuse Angle: Greater than 90° but less than 180°
- *(Note: We won’t see straight or reflex angles here, as clocks typically show angles < 180° for this kind of exercise.)*

Each clock face is 360°, divided into 12 hours → Each hour mark = 30° (360° ÷ 12).
Each minute mark = 6° (360° ÷ 60).

We’ll estimate the angle between the hour and minute hands visually or with simple math.

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## ✔ SOLUTIONS:

1) Clock showing 3:00

- Hour hand at 3, minute hand at 12 → exactly 90° apart.
✔ Right Angle

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2) Clock showing approximately 10:10

- Minute hand at 2 (10 min = 60° from 12)
- Hour hand slightly past 10 → ~300° + (10/60)*30° = 305°
- Difference ≈ |305 - 60| = 245° → but we take the smaller angle → 360 - 245 = 115°
✔ Obtuse Angle

*(Alternatively, visually — it’s clearly more than 90° but less than 180°)*

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3) Clock showing approximately 2:10

- Minute hand at 2 → 60°
- Hour hand just past 2 → ~60° + (10/60)*30° = 65°
- Difference ≈ |65 - 60| = 5° → wait, that can’t be right.

Actually, let’s correct:
At 2:10:
- Minute hand at 2 → 60°
- Hour hand: at 2 o’clock = 60°, plus 10 minutes → moves 5° (since 30° per hour = 0.5° per minute → 10 × 0.5 = 5°) → so hour hand at 65°
→ Angle = |65 - 60| = 5° → too small? That doesn’t match the image.

Looking at the image again — the hour hand is closer to 2, minute hand at 2 — actually, the angle looks very small, maybe around 5–10°.

✔ Acute Angle

*(Visually, it’s a very narrow angle — definitely acute.)*

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4) Clock showing approximately 10:55

- Minute hand at 11 → 330°
- Hour hand near 11 → since 55 min, hour hand is almost at 11 → 330° + (55/60)*30°? Wait — no.

At 10:55:
- Hour hand: 10 o’clock = 300°, plus 55 min → 55 × 0.5 = 27.5° → so 327.5°
- Minute hand: 55 min → 55 × 6 = 330°
→ Difference = |330 - 327.5| = 2.5° → very small!

✔ Acute Angle

*(Visually, the hands are almost overlapping — very small angle.)*

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5) Clock showing approximately 1:10

- Minute hand at 2 → 60°
- Hour hand: 1 o’clock = 30°, plus 10 min → 5° → total 35°
→ Angle = |60 - 35| = 25°

✔ Acute Angle

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6) Clock showing 9:00

- Hour hand at 9, minute hand at 12 → 90° apart (each hour = 30°, 3 hours apart → 3×30=90°)

✔ Right Angle

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7) Clock showing approximately 10:50

- Minute hand at 10 → 300°
- Hour hand: 10 o’clock = 300°, plus 50 min → 50 × 0.5 = 25° → so 325°
→ Angle = |325 - 300| = 25°

✔ Acute Angle

*(Visually, hands are close together — acute.)*

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8) Clock showing 12:30

- Minute hand at 6 → 180°
- Hour hand halfway between 12 and 1 → 15° (since 30° per hour → half = 15°)
→ Angle = |180 - 15| = 165°

✔ Obtuse Angle

*(Clearly greater than 90°, less than 180°)*

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9) Clock showing approximately 3:45

- Minute hand at 9 → 270°
- Hour hand: 3 o’clock = 90°, plus 45 min → 45 × 0.5 = 22.5° → total 112.5°
→ Angle = |270 - 112.5| = 157.5° → or the smaller angle is 360 - 157.5 = 202.5° → no, we always take the smaller one.

Wait — better way: The difference is 157.5°, which is less than 180° → so that’s the angle.

✔ Obtuse Angle

*(Visually — it’s wide, but not straight — obtuse.)*

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## 🎯 Final Answers:

1) Right Angle
2) Obtuse Angle
3) Acute Angle
4) Acute Angle
5) Acute Angle
6) Right Angle
7) Acute Angle
8) Obtuse Angle
9) Obtuse Angle

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✔ Summary Table:

| Clock # | Angle Type |
|---------|----------------|
| 1 | Right |
| 2 | Obtuse |
| 3 | Acute |
| 4 | Acute |
| 5 | Acute |
| 6 | Right |
| 7 | Acute |
| 8 | Obtuse |
| 9 | Obtuse |

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Let me know if you’d like a printable version or visual diagrams for each clock! 😊