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)°.
A triangle’s interior angles add up to 180°. Drawing diagonals from one vertex divides an n-gon into n − 2 triangles, so their combined angle measure is 180(n − 2)°. Therefore, the correct choice is D, 180(n − 2).
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