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(n−2)180∘
In the proof, a pentagon will be considered. However, the proof is valid for any polygon.
For any pentagon, two non-intersecting diagonals can be drawn to divide the pentagon into three triangles. In the case of an arbitrary polygon with n vertices, n−3 non-intersecting diagonals can be drawn to divide the polygon into n−2 triangles.
P=(n−2)180∘