The angle formed by the hands of a clock at $2:15$ is:
$\textbf{(A)}\ 30^\circ \qquad \textbf{(B)}\ 27\frac{1}{2}^\circ\qquad  \textbf{(C)}\ 157\frac{1}{2}^\circ\qquad  \textbf{(D)}\ 172\frac{1}{2}^\circ\qquad \textbf{(E)}\ \text{none of these}$
To find the angle of the clock, we first have to determine where the hands are. The time is $2.25$ hours, so the hour hand would be $62.5$ degrees clockwise. As the clock is a quarter of the way through the hour, the minute hand is $90$ degrees clockwise.
Thus, we can say that the angle formed by the hands is $90 - 62.5 = \boxed{\textbf{(B) } 27\frac{1}{2}}$ degrees.