What is the degree measure of the smaller angle formed by the hands of a clock at 10 o'clock?

$\textbf{(A)}\ 30 \qquad \textbf{(B)}\ 45 \qquad \textbf{(C)}\ 60 \qquad \textbf{(D)}\ 75 \qquad \textbf{(E)}\ 90$
At $10:00$, the hour hand will be on the $10$ while the minute hand on the $12$.
This makes them $\frac{1}{6}$th of a circle apart, and $\frac{1}{6}\cdot360^{\circ}=\boxed{\textbf{(C) } 60}$.