Question

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:

Answer 1

1.n-3

2.n-2

3.180

4.180(n-2)

ON EDG

Answer 2

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)°.