Find the number of right angles turned through by the hour hand of a clock when it goes from 3 to 12.

Options

A. 1
B. 2
C. 3
D. 4

Answer

To find the number of right angles turned through by the hour hand of a clock when it goes from 3 to 12, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Position of the Clock Hands**:
- The hour hand starts at the 3 o'clock position and moves to the 12 o'clock position.

2. **Identify the Movement**:
- The hour hand moves clockwise from 3 to 12.

3. **Count the Hour Intervals**:
- From 3 to 12, the hour hand passes through the following hours: 4, 5, 6, 7, 8, 9, 10, 11.
- This is a total of 9 hours.

4. **Calculate the Angle Turned**:
- The total angle turned by the hour hand in one complete revolution (12 hours) is 360 degrees.
- Therefore, the angle turned in one hour is \( \frac{360 \text{ degrees}}{12 \text{ hours}} = 30 \text{ degrees/hour} \).
- For 9 hours, the angle turned is \( 9 \times 30 = 270 \text{ degrees} \).

5. **Determine the Number of Right Angles**:
- A right angle is 90 degrees.
- To find the number of right angles in 270 degrees, we divide 270 by 90:
\[ \frac{270 \text{ degrees}}{90 \text{ degrees/right angle}} = 3 \text{ right angles} \]

6. **Conclusion**:
- Therefore, the number of right angles turned through by the hour hand of the clock when it goes from 3 to 12 is **3**.