For a natural number n≥3, 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?
combinatoricscombinatorial geometrypolygondiagonals