SG. 1 The acute angle between the 2 hands of a clock at 3:30 p.m. is $p^{\circ}$. Find $p$.
At 3:00 p.m., the angle between the arms of the clock $=90^{\circ}$
From 3:00 p.m. to 3:30 p.m., the hour-hand had moved $360^{\circ} \times \frac{1}{12} \times \frac{1}{2}=15^{\circ}$.
The minute hand had moved $180^{\circ}$.
$$
p=180-90-15=75
$$