Find the smaller angle formed between the hour hand and the minute hand of a clock when the time is 8 o'clock.

Answer

To find the smaller angle formed between the hour hand and the minute hand of a clock when the time is 8 o'clock, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the positions of the hands at 8 o'clock**:
- At 8 o'clock, the hour hand points directly at the 8, and the minute hand points directly at the 12.

2. **Calculate the angle for the hour hand**:
- The clock is divided into 12 hours, and a complete rotation (360 degrees) is made in 12 hours.
- Therefore, the angle moved by the hour hand for each hour is:
\[ \text{Angle per hour} = \frac{360 \text{ degrees}}{12 \text{ hours}} = 30 \text{ degrees per hour} \]
- At 8 o'clock, the hour hand has moved:
\[ \text{Angle of hour hand} = 8 \text{ hours} \times 30 \text{ degrees/hour} = 240 \text{ degrees} \]

3. **Calculate the angle for the minute hand**:
- The minute hand completes a full rotation (360 degrees) in 60 minutes.
- Therefore, at 0 minutes (which is 8:00), the angle of the minute hand is:
\[ \text{Angle of minute hand} = 0 \text{ degrees} \]

4. **Find the difference between the two angles**:
- The angle between the hour hand and the minute hand is:
\[ \text{Angle between hands} = |240 \text{ degrees} - 0 \text{ degrees}| = 240 \text{ degrees} \]

5. **Determine the smaller angle**:
- The smaller angle formed between the two hands can be found by subtracting the larger angle from 360 degrees:
\[ \text{Smaller angle} = 360 \text{ degrees} - 240 \text{ degrees} = 120 \text{ degrees} \]

### Final Answer:
The smaller angle formed between the hour hand and the minute hand at 8 o'clock is **120 degrees**.