Regular polygons with whole-degree interior angles

For how many integers $n\ge3$ does a regular polygon with $n$ sides have an interior angle that is a whole number of degrees?

$22$. The interior angle is $180-\tfrac{360}{n}$, an integer exactly when $n\mid360$. Since $360=2^3\cdot3^2\cdot5$ has $24$ divisors, removing $n=1$ and $n=2$ leaves $22$.