We are given an n-gon, which has n sides and n vertices. If we choose one of the vertices, we can draw diagonals. These diagonals form triangles. The sum of the interior angle measures of a triangle is degrees. n – 2 triangles would have an interior angle measure sum of . Therefore, the sum of the measures of the interior angles of an n-gon is 180(n – 2)°.
Each triangle has an interior angle sum of 180°. Drawing diagonals from one vertex of an n-gon divides it into n − 2 triangles, so the polygon’s interior angle sum is 180(n − 2)°. The correct choice is n − 2.
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