What is the angle between the two hands of a clock when the time shown by the clock is 8 p.m.?(in degrees)

Options

A. 240
B. 120
C. 60
D. 50

Answer

To find the angle between the hour and minute hands of a clock at 8 p.m., we can use the formula:

\[ \text{Angle} = \frac{1}{2} \left| 60h - 11m \right| \]

where \( h \) is the hour and \( m \) is the minute.

### Step-by-Step Solution:

1. **Identify the values of \( h \) and \( m \)**:
- At 8 p.m., the hour \( h = 8 \).
- The minute \( m = 0 \) (since it is exactly 8:00).

2. **Substitute the values into the formula**:
\[ \text{Angle} = \frac{1}{2} \left| 60 \times 8 - 11 \times 0 \right| \]

3. **Calculate \( 60h \)**:
\[ 60 \times 8 = 480 \]

4. **Calculate \( 11m \)**:
\[ 11 \times 0 = 0 \]

5. **Substitute these values back into the formula**:
\[ \text{Angle} = \frac{1}{2} \left| 480 - 0 \right| = \frac{1}{2} \left| 480 \right| \]

6. **Calculate the absolute value**:
\[ \left| 480 \right| = 480 \]

7. **Final calculation**:
\[ \text{Angle} = \frac{1}{2} \times 480 = 240 \text{ degrees} \]

### Conclusion:
The angle between the hour hand and the minute hand at 8 p.m. is **240 degrees**.

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