If the number of sides of a regular polygon increases by 9, then each angle of the polygon increases by $9^{\circ}$. Which polygon is this?
If the polygon in question has $n$ sides, then according to the problem,

$$
\frac{(n-2) 180}{n}+9=\frac{(n+7) 180}{n+9}
$$

or

$$
n^{2}+9 n=360
$$

the positive root of which is: $n=15$.

(Dénes Miklós, Budapest, V. district real.)

Number of solutions: 28.