What is the angle between the hour and minute hands of a clock at 3 o'clock?

At 3 o'clock, the minute hand points exactly at 12 and the hour hand points exactly at 3.
The total dial of a clock is $360^{\circ }$ divided into 12 hours, which means each hour gap represents:

$$\frac{360^{\circ }}{12}=30^{\circ }$$

The hands are exactly 3 hour gaps apart:

$$\text{Angle}=3\times 30^{\circ }=90^{\circ }$$