AIME 1990 Problem 3

Let $P_1^{}$ be a regular $r~\text{gon}$ and $P_2^{}$ be a regular $s~\text{gon}$ $(r\geq s\geq 3)$ such that each interior angle of $P_1^{}$ is $\frac{59}{58}$ as large as each interior angle of $P_2^{}$. What's the largest possible value of $s_{}^{}$?