Answer
$22^\circ30'$
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 9:45, the smaller angle formed by the hands contains $\frac{3}{4}$ division, thus the angle is $\alpha=\frac{3\times30^\circ}{4}=22.5^\circ=22^\circ30'$
