Practice worksheet for drawing clock times and identifying angles.

To solve this problem, we need to do two things for each time:
1. Draw the hands on the clock face to show the correct time.
2. Name the angle formed by the two hands. The options are acute (less than 90°), right (exactly 90°), straight (exactly 180°), or obtuse (more than 90° but less than 180°).

Let’s go one by one:

---

1. 9:15
- Hour hand: At 9:15, the hour hand is a little past 9 (since 15 minutes is 1/4 of an hour).
- Minute hand: Points at 3 (because 15 minutes = 3 on the clock).
- Angle between 9 and 3 is 180° — that’s a straight line.
→ But wait! The hour hand has moved slightly toward 10. So the angle is *slightly less* than 180°.
→ That makes it obtuse.

2. 2:35
- Hour hand: Past 2, closer to 3 (35 minutes is more than half an hour).
- Minute hand: Points at 7 (35 minutes = 7 on the clock).
- From 2 to 7 is 5 hours → 5 × 30° = 150° (each hour mark is 30° apart).
- Since the hour hand has moved toward 3, the angle is a bit less than 150° — still more than 90°.
→ Obtuse

3. 6:25
- Hour hand: Past 6, about halfway to 7 (25 minutes is almost half an hour).
- Minute hand: Points at 5 (25 minutes = 5 on the clock).
- From 5 to 6 is 30°, plus the extra movement of the hour hand → roughly 40–50°? Wait, let’s think again.
Actually, from minute hand at 5 to hour hand past 6: that’s more than 30° but less than 90°.
→ Acute

Wait — correction: At 6:25, the minute hand is at 5, and the hour hand is between 6 and 7. The angle between them is from 5 to just past 6 → that’s about 30° + a little → still under 90°.
→ Acute

4. 8:00
- Hour hand: Exactly on 8.
- Minute hand: Exactly on 12.
- From 8 to 12 is 4 hours → 4 × 30° = 120°.
→ Obtuse

5. 12:45
- Hour hand: Almost at 1 (since 45 minutes is 3/4 of the way to 1).
- Minute hand: Points at 9.
- From 9 to almost 1: that’s 4 hours minus a bit → 120° minus a little → still over 90°.
→ Obtuse

6. 12:30
- Hour hand: Halfway between 12 and 1.
- Minute hand: Points at 6.
- From 6 to halfway between 12 and 1: that’s 180° minus 15° (half of 30°) → 165°.
→ Obtuse

7. 10:20
- Hour hand: Past 10, about 1/3 toward 11 (20 minutes is 1/3 of an hour).
- Minute hand: Points at 4.
- From 4 to 10 is 6 hours → 180°, but the hour hand has moved toward 11, so the angle is less than 180°.
Actually, from 4 to 10 is 180°, but since the hour hand is past 10, the angle between minute hand at 4 and hour hand past 10 is less than 180° — how much?
From 4 to 10 is 180°, but now the hour hand is 1/3 of the way to 11, so the angle is 180° - 10° = 170°? Still obtuse.
Wait — actually, the smaller angle between them: from 4 to 10 is 180°, but if we go the other way, from 4 to 10 clockwise is 180°, counterclockwise is also 180° — no, that can’t be.

Better way: Total circle is 360°. Each number is 30°.
At 10:20:
- Minute hand at 4 → 4 × 30° = 120° from 12.
- Hour hand: at 10 + 20/60 = 10 + 1/3 → 10.333... × 30° = 310° from 12.
Angle between them: |310 - 120| = 190° → but we take the smaller angle, so 360° - 190° = 170° → still obtuse.

But wait — 170° is obtuse? Yes, because obtuse is >90° and <180°. 170° fits.

→ Obtuse

8. 5:00
- Hour hand: On 5.
- Minute hand: On 12.
- From 5 to 12 is 7 hours → 7 × 30° = 210° → but smaller angle is 360° - 210° = 150°.
→ Obtuse

9. 1:15
- Hour hand: Past 1, about 1/4 toward 2.
- Minute hand: Points at 3.
- From 1.25 to 3: that’s 1.75 hours → 1.75 × 30° = 52.5°.
→ Acute

10. 3:30
- Hour hand: Halfway between 3 and 4.
- Minute hand: Points at 6.
- From 3.5 to 6: that’s 2.5 hours → 2.5 × 30° = 75°.
→ Acute

11. 1:50
- Hour hand: Almost at 2 (50 minutes is 5/6 of the way).
- Minute hand: Points at 10.
- From 10 to almost 2: that’s 4 hours minus a bit → 120° minus a little → still over 90°.
Calculate:
Minute hand at 10 → 300° from 12.
Hour hand at 1 + 50/60 = 1.833... → 1.833 × 30° = 55° from 12.
Angle: |300 - 55| = 245° → smaller angle is 360° - 245° = 115°.
→ Obtuse

12. 7:15
- Hour hand: Past 7, 1/4 toward 8.
- Minute hand: Points at 3.
- From 3 to 7.25: that’s 4.25 hours → 4.25 × 30° = 127.5°.
→ Obtuse

Wait — let me double-check 7:15.
Minute hand at 3 → 90° from 12.
Hour hand at 7 + 15/60 = 7.25 → 7.25 × 30° = 217.5° from 12.
Angle: |217.5 - 90| = 127.5° → yes, obtuse.

---

Now, let’s list all answers clearly:

1. 9:15 → Obtuse
2. 2:35 → Obtuse
3. 6:25 → Acute
4. 8:00 → Obtuse
5. 12:45 → Obtuse
6. 12:30 → Obtuse
7. 10:20 → Obtuse
8. 5:00 → Obtuse
9. 1:15 → Acute
10. 3:30 → Acute
11. 1:50 → Obtuse
12. 7:15 → Obtuse

Wait — I think I made a mistake on 6:25.

Let me recalculate 6:25 carefully.

At 6:25:
- Minute hand: at 5 → 5 × 30° = 150° from 12.
- Hour hand: at 6 + 25/60 = 6.4167 → 6.4167 × 30° = 192.5° from 12.
Angle between them: |192.5 - 150| = 42.5° → which is less than 90° → Acute. Correct.

Another check: 3:30
- Minute hand at 6 → 180°
- Hour hand at 3.5 → 105°
Angle: |180 - 105| = 75° → Acute. Correct.

1:15:
- Minute hand at 3 → 90°
- Hour hand at 1.25 → 37.5°
Angle: |90 - 37.5| = 52.5° → Acute. Correct.

All others seem correct.

Final list:

1. 9:15 — Obtuse
2. 2:35 — Obtuse
3. 6:25 — Acute
4. 8:00 — Obtuse
5. 12:45 — Obtuse
6. 12:30 — Obtuse
7. 10:20 — Obtuse
8. 5:00 — Obtuse
9. 1:15 — Acute
10. 3:30 — Acute
11. 1:50 — Obtuse
12. 7:15 — Obtuse

Note: For drawing, the student should draw the hands accordingly, but since we’re only naming angles here, we focus on that.

Final Answer:
9:15 - obtuse, 2:35 - obtuse, 6:25 - acute, 8:00 - obtuse, 12:45 - obtuse, 12:30 - obtuse, 10:20 - obtuse, 5:00 - obtuse, 1:15 - acute, 3:30 - acute, 1:50 - obtuse, 7:15 - obtuse