What is the degree measure of the smaller angle between the hour hand and the minute hand of a clock at exactly 2: 30 p. m. on a 12-hour analog clock?

105°

Step-by-step explanation:

We are supposed to find the angle between the hour hand and the minute hand at a time of 2:30 in a 12 hour analog clock.

So, we have 12 segments in a clock , each segment corresponding to an hour.

Angle of each segment would be :-

At 2:30 the minute hand will be facing 6 hour direction and the hour hand between hours 2 and 3.

So the angle between them would be

So the angle between the hour and the minute hand at time 2:30 is 105°.