How many right angles are formed when hour hand of a clock moves from :
(i) 2 to 8
(ii) 6 to 9
(iii) 10 to 4

Answer

To solve the question of how many right angles are formed when the hour hand of a clock moves from different positions, we will analyze each case step by step.

### Step-by-Step Solution:

**(i) From 2 to 8:**
1. **Identify the positions on the clock:** The hour hand starts at 2 and moves to 8.
2. **Calculate the total movement:** The hour hand moves from 2 to 8, which is a total of 6 hours (2 → 3 → 4 → 5 → 6 → 7 → 8).
3. **Determine the angles formed:**
- From 2 to 3: 1 right angle (90 degrees)
- From 3 to 4: 1 right angle (90 degrees)
- From 4 to 5: 1 right angle (90 degrees)
- From 5 to 6: 1 right angle (90 degrees)
- From 6 to 7: 1 right angle (90 degrees)
- From 7 to 8: 1 right angle (90 degrees)
4. **Total right angles formed:** 5 right angles.

**(ii) From 6 to 9:**
1. **Identify the positions on the clock:** The hour hand starts at 6 and moves to 9.
2. **Calculate the total movement:** The hour hand moves from 6 to 9, which is a total of 3 hours (6 → 7 → 8 → 9).
3. **Determine the angles formed:**
- From 6 to 7: 1 right angle (90 degrees)
- From 7 to 8: 1 right angle (90 degrees)
- From 8 to 9: 1 right angle (90 degrees)
4. **Total right angles formed:** 3 right angles.

**(iii) From 10 to 4:**
1. **Identify the positions on the clock:** The hour hand starts at 10 and moves to 4.
2. **Calculate the total movement:** The hour hand moves from 10 to 4, which is a total of 6 hours (10 → 11 → 12 → 1 → 2 → 3 → 4).
3. **Determine the angles formed:**
- From 10 to 11: 1 right angle (90 degrees)
- From 11 to 12: 1 right angle (90 degrees)
- From 12 to 1: 1 right angle (90 degrees)
- From 1 to 2: 1 right angle (90 degrees)
- From 2 to 3: 1 right angle (90 degrees)
- From 3 to 4: 1 right angle (90 degrees)
4. **Total right angles formed:** 5 right angles.

### Final Answer:
- From 2 to 8: **5 right angles**
- From 6 to 9: **3 right angles**
- From 10 to 4: **5 right angles**