The angle between the minutes hand and hours hand in a clock, at 12:30 p.m. is

Options

A. `gt0^(@)`
B. `gt30^(@)`
C. `gt60^(@)`
D. `gt90^(@)`

Answer

To find the angle between the minute hand and the hour hand of a clock at 12:30 p.m., we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Position of the Hands**:
- At 12:30, the hour hand is halfway between 12 and 1, and the minute hand is pointing at 6.

2. **Calculate the Position of the Hour Hand**:
- The hour hand moves 30 degrees for each hour (360 degrees / 12 hours = 30 degrees per hour).
- At 12:00, the hour hand is at 0 degrees.
- By 12:30, the hour hand has moved halfway to the 1 o'clock position.
- Therefore, at 12:30, the hour hand is at:
\[ 0 + \left(\frac{1}{2} \times 30\right) = 15 \text{ degrees} \]

3. **Calculate the Position of the Minute Hand**:
- The minute hand moves 6 degrees for each minute (360 degrees / 60 minutes = 6 degrees per minute).
- At 30 minutes, the minute hand is at:
\[ 30 \times 6 = 180 \text{ degrees} \]

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:
\[ \text{Angle} = |180 - 15| = 165 \text{ degrees} \]

5. **Conclusion**:
- Therefore, the angle between the minute hand and the hour hand at 12:30 p.m. is **165 degrees**.