How many sides does a regular polygon have if the measure of the exterior angle is 9 degrees less than the number of sides?
Let the number of sides we are looking for be denoted by $n$. The measure of each exterior angle of a regular $n$-sided polygon is $\frac{360^{\circ}}{n}$, thus

$$
\frac{360}{n}=n-9
$$

which simplifies to

$$
n^{2}-9 n-360=0
$$

from which we get

$$
n_{1}=24 \quad\left[n_{2}=-15\right]
$$

Only the positive integer root makes sense. Therefore, the regular polygon has 24 sides.

Szendrei István (Kunszentmiklós, Damjanich g. I. o. t.)