Find the number of right angles turned through by the hour hand of a clock when it goes from
3 to 6

Answer

To find the number of right angles turned through by the hour hand of a clock when it goes from 3 to 6, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Clock Positions**:
- The clock has 12 positions, each representing an hour.
- The positions are: 12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11.

2. **Identifying the Starting and Ending Points**:
- The hour hand starts at 3 and moves to 6.
- We need to determine how many hour positions it passes through.

3. **Counting the Hour Positions**:
- From 3 to 4 is 1 hour.
- From 4 to 5 is another hour.
- From 5 to 6 is yet another hour.
- Therefore, the hour hand moves through 3 hour positions (3 to 4, 4 to 5, and 5 to 6).

4. **Calculating the Degrees Turned**:
- The total degrees in a clock is 360 degrees.
- Since there are 12 hours on the clock, each hour represents:
\[ \text{Degrees per hour} = \frac{360 \text{ degrees}}{12 \text{ hours}} = 30 \text{ degrees per hour} \]

5. **Finding the Total Degrees for 3 Hours**:
- For 3 hours, the total degrees turned by the hour hand is:
\[ \text{Total degrees} = 3 \text{ hours} \times 30 \text{ degrees/hour} = 90 \text{ degrees} \]

6. **Determining the Number of Right Angles**:
- A right angle is 90 degrees.
- Since the hour hand turned 90 degrees from 3 to 6, it turned through:
\[ \text{Number of right angles} = \frac{90 \text{ degrees}}{90 \text{ degrees/right angle}} = 1 \text{ right angle} \]

### Final Answer:
The hour hand of the clock turns through **1 right angle** when it goes from 3 to 6.

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