An n-sided pofygon (commonly shortened to n-gon) is a closed planar figure bounded by n straight sides no two of which intersect unless they are adjacent, in which case they intersect just at a vertex. Thus, a 3-gon is a triangle,
a 4-gon is a quadrilateral, a 5-gon is a pentagon, and so on. An n-gon is convex if the line joining any pair of nonadjacent vertices lies entirely within the figure. A rectangle, for example, is convex. Prove that the sum of the interior angles of a convex n-gon is (n − 2)180° for all n ≥ 3.
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