What will be the angle between minute end and hour end in a Clock at 7 : 20?

Question

Accepted Answer

To determine the angle between the minute hand and the hour hand of a clock at 7:20, we can use the following method:

1. **Calculate the position of the hour hand:**
   - Each hour on the clock represents 30 degrees (360 degrees/12 hours).
   - At 7:00, the hour hand is at 210 degrees (7 hours * 30 degrees/hour).
   - By 7:20, the hour hand has moved further. Since each minute moves the hour hand by 0.5 degrees (30 degrees/hour divided by 60 minutes), in 20 minutes, the hour hand moves an additional 10 degrees (20 minutes * 0.5 degrees/minute).
   - Therefore, at 7:20, the hour hand is at 220 degrees (210 degrees + 10 degrees).

2. **Calculate the position of the minute hand:**
   - Each minute on the clock represents 6 degrees (360 degrees/60 minutes).
   - At 20 minutes, the minute hand is at 120 degrees (20 minutes * 6 degrees/minute).

3. **Calculate the angle between the two hands:**
   - The angle between the hour hand and the minute hand is the absolute difference between their positions.
   - Angle = |220 degrees - 120 degrees| = 100 degrees.

Therefore, the angle between the minute hand and the hour hand at 7:20 is 100 degrees, which corresponds to Option 2.

**Explanation for why other options are incorrect:**

- **Option 1 (160°):** This angle is incorrect because the calculation shows that the angle is 100 degrees, not 160 degrees.
- **Option 3 (260°):** This angle is incorrect because it exceeds the maximum possible angle between the two hands on a clock, which is 180 degrees.
- **Option 4 (120°):** This angle is incorrect because the calculation clearly shows the angle is 100 degrees, not 120 degrees.

In conclusion, the correct answer is Option 2, 100°, based on the calculations provided.