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)°. word bank: n - 2n - 3180 (n - 2)180 blank 1:

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.

Answers:

1. If we choose one of the vertices, we can draw n-3 diagonals.

2. These diagonals form n-2 triangles.

3. The sum of the interior angle measures of a triangle is 180 degrees.

4. n – 2 triangles would have an interior angle measure sum of 180 degrees.

5. Therefore, the sum of the measures of the interior angles of an n-gon is 180(n – 2)°.

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step-by-step explanation:

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