Answer
$125^\circ$
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 6:10, the smaller angle formed by the hands contains $4\frac{1}{6}=\frac{25}{6}$ divisions, thus the angle is $\alpha=\frac{25\times30^\circ}{6}=125^\circ$
