The angle between the minute hand and hour of a clock, when the time is 7 : 20 is equal to

Options

A. `45^@`
B. `90^@`
C. `100^@`
D. `120^@`

Answer

To find the angle between the minute hand and the hour hand of a clock at 7:20, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Movement of the Clock Hands**:
- The hour hand completes a full circle (360 degrees) in 12 hours.
- The minute hand completes a full circle (360 degrees) in 60 minutes.

2. **Calculate the Position of the Hour Hand**:
- At 7:00, the hour hand is at 7. Each hour represents 30 degrees (since 360 degrees / 12 hours = 30 degrees per hour).
- By 7:20, the hour hand has moved further. In 20 minutes, the hour hand moves:
\[ \text{Degrees moved by hour hand} = \left(\frac{20}{60}\right) \times 30 = 10 \text{ degrees} \]
- Therefore, the position of the hour hand at 7:20 is:
\[ 7 \times 30 + 10 = 210 + 10 = 220 \text{ degrees} \]

3. **Calculate the Position of the Minute Hand**:
- The minute hand at 20 minutes is:
\[ \text{Degrees moved by minute hand} = \left(\frac{20}{60}\right) \times 360 = 120 \text{ degrees} \]

4. **Find the Angle Between the Two Hands**:
- The angle between the hour hand and the minute hand is the absolute difference between their positions:
\[ \text{Angle} = |220 - 120| = 100 \text{ degrees} \]

5. **Conclusion**:
- The angle between the minute hand and the hour hand at 7:20 is 100 degrees.