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n-3 internal diagonals in a non self-intersecting n-gon , cut into n-2 triangles

Source: 2022 Baltic Way p8

November 13, 2022

combinatoricscombinatorial geometrypolygondiagonals

Problem Statement

For a natural number

n \ge 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

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