The angle formed by the hour hand and the minute-hand of a clock at 2:15 p.m. is

Options

A. `27"" (1)/(2)"" ^(@)`
B. `45^(@)`
C. `22"" (1)/(2)""^(@)`
D. `30^(@)`

Answer

To find the angle formed by the hour hand and the minute hand of a clock at 2:15 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 2:15 p.m., the hour \( h = 2 \) and the minutes \( m = 15 \).

2. **Substitute the values into the formula**:
\[ \text{Angle} = \frac{1}{2} \left| 60 \times 2 - 11 \times 15 \right| \]

3. **Calculate \( 60h \)**:
\[ 60 \times 2 = 120 \]

4. **Calculate \( 11m \)**:
\[ 11 \times 15 = 165 \]

5. **Substitute these results back into the equation**:
\[ \text{Angle} = \frac{1}{2} \left| 120 - 165 \right| \]

6. **Calculate \( 120 - 165 \)**:
\[ 120 - 165 = -45 \]

7. **Take the absolute value**:
\[ \left| -45 \right| = 45 \]

8. **Calculate the final angle**:
\[ \text{Angle} = \frac{1}{2} \times 45 = 22.5 \text{ degrees} \]

### Final Answer:
The angle formed by the hour hand and the minute hand at 2:15 p.m. is \( 22.5 \) degrees.