Question

At 3:30 P.M. the angle between the hands of a
clock is

Answer 1

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.

Answer 2

Well, the "hour" hand is 3.5*30=105 degrees from the "12" marking (30 degrees per hour), while the "minute" hand is 30*6=180 degrees from the "12" marking (6 degs per minute). The difference, that is, 75 degrees, is our angle. The other difference would have been over 180, which is not important for us.