Baltic Way 2022 · Problem 8

For a natural number $n\ge3$, we draw $n-3$ internal diagonals in a non self-intersecting, but not necessarily convex, $n$-gon, cutting the $n$-gon into $n-2$ triangles. It is known that the value (in degrees) of any angle in any of these triangles is a natural number and no two of these angle values are equal. What is the largest possible value of $n$?