I3.1 The acute angle formed by the hands of a clock at 2:15 is $\left(18 \frac{1}{2}+a\right)^{\circ}$. Find $a$.
At 2:00, the angle between the arms of the clock $=60^{\circ}$
From 2:00 to 2:15, the hour-hand had moved $360^{\circ} \times \frac{1}{12} \times \frac{1}{4}=7.5^{\circ}$
The minute hand had moved $90^{\circ}$
$$
\begin{array}{l}
18.5+a=90-(60+7.5)=22.5 \\
a=4
\end{array}
$$