Answer
$7^\circ30'$
Work Step by Step
1. There are $12$ hourly divisions on the clock face, each division equals to $\frac{360^\circ}{12}=30^\circ$
2. At 3:15, the smaller angle formed by the hands is $\frac{1}{4}$ division, thus the angle is $\alpha=\frac{30^\circ}{4}=7.5^\circ=7^\circ30'$
