Angle Measures of Polygons

Question 1

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)°.

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D: n – 3

Question 2

The sign has sides, so it is .

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C: 8

Question 3

An interior angle of a regular polygon has a measure of 120°. What type of polygon is it?

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B: hexagon

Question 4

For a convex n-gon, interior and exterior angles form angles, whose measures sum to 180°.

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A: adjacent

Question 5

x =

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A: 14

Question 6

The polygon is and is .

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D: an octagon

Question 7

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)°.

Revolt · Accepted Answer

D: n – 2

Question 8

The sign has sides, so it is .

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C: an octagon

Question 9

Because we have an n-gon, the sum of the measures of these linear pairs, one exterior angle at each vertex, is °.

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C: 180n

Question 10

The polygon is and is .

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B: convex

Angle Measures of Polygons Answers

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