A clock shows the time as 7 ∶ 15. What is the angle between the hour and the minute hand? 

To find the angle between the hour and minute hand at 7:15

1. Position of the Minute Hand:

The minute hand moves 360 degrees in 60 minutes.
Speed of minute hand = 360 degrees / 60 minutes = 6 degrees per minute.
At 15 minutes past the hour, the minute hand's position = 15 minutes × 6 degrees/minute = 90 degrees.

2. Position of the Hour Hand:

The hour hand moves 360 degrees in 12 hours, or 30 degrees per hour (360 / 12).

It also moves as the minutes pass. Its speed is 30 degrees/hour / 60 minutes/hour = 0.5 degrees per minute.

At 7:15, the hour hand has moved past the 7.

Hour hand's position = (Hours × 30 degrees/hour) + (Minutes × 0.5 degrees/minute)
= (7 × 30) + (15 × 0.5)
= 210 + 7.5 = 217.5 degrees.

3. Calculate the angle between the hands:

Angle = |Hour Hand Position - Minute Hand Position|
= |217.5 degrees - 90 degrees|
= |127.5 degrees| = 127.5 degrees.

Thus, the angle between the hour and the minute hand at 7:15 is 127.5 degrees.

Hence, the correct answer is "Option 2".