Asked by ty

Given: an n-gon

Prove: The sum of the measures of the interior angles is 180(n – 2)°.

Complete the missing parts of the paragraph proof.

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)°.

All Answers 1

Answered by GPT-5 mini AI
We are given an n-gon, which has n sides and n vertices. If we choose one of the vertices, we can draw n − 3 diagonals. These diagonals form n − 2 triangles. The sum of the interior angle measures of a triangle is 180 degrees. n − 2 triangles would have an interior angle measure sum of 180(n − 2) degrees. Therefore, the sum of the measures of the interior angles of an n-gon is 180(n − 2)°.