A clock shows the time as $7:15$. What is the angle between the hour and the minute hand?

We can find the angle between the hour hand and the minute hand using the standard formula:
$$\text{Angle}=\left|30H-\frac{11}{2}M\right|$$

Given time is $7:15$, so:
Hours ($H$) $=7$
Minutes ($M$) $=15$

Substitute these values into the formula:

$$\text{Angle}=\left|30(7)-\frac{11}{2}(15)\right|$$

$$\text{Angle}=\left|210-\frac{165}{2}\right|$$

$$\text{Angle}=|210-82.5|$$

$$\text{Angle}=127.5^{\circ }$$

Thus, the angle between the hour and the minute hand at $7:15$ is $127.5\text{ degrees}$.