An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon?

Answer

To solve the problem of how many degrees the hour hand of a clock rotates from 8 o'clock in the morning to 2 o'clock in the afternoon, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Time Interval**:
- The clock shows 8 o'clock in the morning and we need to find out how far the hour hand moves by the time it shows 2 o'clock in the afternoon.
- The time interval from 8 AM to 2 PM is 6 hours.

2. **Calculate the Degrees Rotated per Hour**:
- A complete rotation of the clock (12 hours) corresponds to 360 degrees.
- Therefore, the degrees rotated by the hour hand in one hour can be calculated as:
\[ \text{Degrees per hour} = \frac{360 \text{ degrees}}{12 \text{ hours}} = 30 \text{ degrees/hour} \]

3. **Calculate the Total Degrees Rotated**:
- Since the hour hand moves 30 degrees for each hour, for 6 hours, the total degrees rotated can be calculated as:
\[ \text{Total degrees} = 30 \text{ degrees/hour} \times 6 \text{ hours} = 180 \text{ degrees} \]

4. **Conclusion**:
- Therefore, the hour hand will rotate 180 degrees from 8 o'clock in the morning to 2 o'clock in the afternoon.

### Final Answer:
The hour hand will rotate **180 degrees**.

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