The angle is degree measure between two hands of a clock at `8 : 30` p.m. is

Options

A. `55^(@)`
B. `66^(@)`
C. `75^(@)`
D. `80^(@)`

Answer

To find the angle between the hour and minute hands of a clock at 8:30 p.m., we can use the formula:

\[ \text{Angle} = |(30H - \frac{11}{2}M)| \]

where \( H \) is the hour and \( M \) is the minutes.

### Step-by-Step Solution:

1. **Identify the values of H and M**:
- Here, \( H = 8 \) (the hour) and \( M = 30 \) (the minutes).

2. **Substitute the values into the formula**:
\[ \text{Angle} = |(30 \times 8 - \frac{11}{2} \times 30)| \]

3. **Calculate \( 30H \)**:
\[ 30 \times 8 = 240 \]

4. **Calculate \( \frac{11}{2}M \)**:
\[ \frac{11}{2} \times 30 = \frac{330}{2} = 165 \]

5. **Subtract the two results**:
\[ \text{Angle} = |240 - 165| = |75| = 75 \text{ degrees} \]

6. **Final Result**:
The angle between the hour and minute hands at 8:30 p.m. is \( 75 \) degrees.