What is the angle made by the hour hand and the minute hand, if the clock shows 9:15 pm ?187.5°172.5°150.5°197.5°

At 9:15, the minute hand is at 3 while the hour hand is 1/4 of the way between 9 and 10.

In a clock, each hour makes 30 degrees (360 degrees / 12 hours = 30 degrees per hour). So, the hour hand at 1/4 past 9 will be 7.5 degrees past the 9 hour mark (30 degrees * 1/4 = 7.5 degrees).

The minute hand at 15 minutes past the hour is at the 3 hour mark, which is 90 degrees (3 hours * 30 degrees per hour = 90 degrees).

So, the angle between the hour and minute hand is 90 degrees (for the minute hand) plus 7.5 degrees (for the hour hand) which equals 97.5 degrees.

However, since the question is asking for the larger angle made by the hour and minute hand, we subtract 97.5 from 360 (since a circle is 360 degrees) to get the larger angle.

So, the larger angle made by the hour and minute hand at 9:15 is 360 - 97.5 = 262.5 degrees.

None of the options provided in the question match this answer.