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

A complete circle of a clock represents $360^{\circ }$ and is divided into $12$ hours.
The angle covered by the hour hand in one hour division is:

$$\text{Angle per hour division}=\frac{360^{\circ }}{12}=30^{\circ }$$

At 3 o'clock:

* The minute hand points exactly at $12$.
* The hour hand points exactly at $3$.

The number of hour divisions between $12$ and $3$ is exactly $3$.

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

Therefore, the angle between the hands is $90^{\circ }$.