Gap between clock hands at 3:15

Find the angle, in degrees, between the minute hand and the hour hand of a clock reading 3:15.

$7.5^\circ$. At 3:15 the minute hand is on the 3. The hour hand moves $30^\circ$ per hour, so after a quarter hour it is $\tfrac14\cdot30^\circ=7.5^\circ$ past the 3.