UNO High School Problem of the Week Competition

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Problem 15

An "n-pointed star" is formed as follows: the sides of a convex polygon are numbered consecutively 1, 2, ..., k , ...., n, n >= 5; for all n values of k, sides k and k + 2 are non-parallel, sides n + 1 and n + 2 being respectively indentical with sides 1 and 2; prolong the n pairs of sides numbered k and k + 2 until they meet. (A figure is shown for the case n = 5).
Let S be the degree-sum of the interior angles at the n points of the star; then S equals?

Solution