$36 \cdot 50$ time $2: 15$, the angle between the hour and minute hands is
(A) $30^{\circ}$.
(B) $5^{\circ}$.
(C) $22.5^{\circ}$.
(D) $7.5^{\circ}$.
(E) $28^{\circ}$.
(2nd American High School Mathematics Examination, 1951)
[Solution] At 2:00, the angle between the minute hand and the hour hand of a clock is $60^{\circ}$. The minute hand rotates at a speed 12 times that of the hour hand.

From 2:00 to 2:15, the minute hand rotates through $90^{\circ}$, during which the hour hand moves $\frac{90^{\circ}}{12}$. Therefore, at 2:15, the angle between the minute hand and the hour hand is
$$
90^{\circ}-\left(60^{\circ}+\frac{90^{\circ}}{12}\right)=22.5^{\circ} .
$$

Thus, the answer is $(C)$.