What is the angle made by the hour hand and the minute hand, if the clock shows 9:15 pm ?

To find the angle between the hour and minute hand at 9:15, you can follow these steps:

1. First, calculate the angle covered by the hour hand. In one hour, the hour hand covers 30 degrees (360 degrees / 12 hours = 30 degrees per hour). At 9:15, the hour hand is a quarter of the way between 9 and 10. So, it has covered 9 hours and 15 minutes, which is 9.25 hours. Multiply this by 30 to get the angle covered by the hour hand: 9.25 hours * 30 degrees/hour = 277.5 degrees.

2. Next, calculate the angle covered by the minute hand. In one minute, the minute hand covers 6 degrees (360 degrees / 60 minutes = 6 degrees per minute). At 15 minutes, the minute hand has covered 15 * 6 = 90 degrees.

3. Subtract the smaller angle from the larger one to find the angle between the two hands: 277.5 degrees - 90 degrees = 187.5 degrees.

However, the angle between the hands of a clock is usually considered to be the smaller angle. So, subtract this from 360 degrees to get the smaller angle: 360 degrees - 187.5 degrees = 172.5 degrees.

So, the angle between the hour hand and the minute hand at 9:15 is 172.5 degrees.