Find the angle between the hands of a clock at

3: 30 o'clock.

The angle between any two divisions is 30 degree.

Angular speed of hour hand = 30 degree / hour = 0.5 degree/minute.

In 30 minutes , the angle swept by hour hand is 30 x 0.5 = 15 degree.

At 3:30 , the minute hand is at number 6.

At 3:00 the hour hand was at number 3.

Now it has moved 15 degree.

Hence the angle between the two is ( 90 -15) = 75 degree.