Angle Measures of Polygons

Question 1

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

Revolt · Accepted Answer

adjacent; For a convex n-gon, interior and exterior angles form angles, whose measures sum to 180°.: adjacent; Because we have an n-gon, the sum of the measures of these linear pairs, one exterior angle at each vertex, is °.: 180n; The sum of the measures of the interior angles is by the polygon interior angle sum theorem.: 180(n – 2); To find the measure of the exterior angles, we can subtract the sum of the measures of the interior angles from the sum of the measures of the linear pairs. Therefore, we have , which is equal to 360°: 180n – 180(n – 2)

Question 2

The sign has sides, so it is .

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an octagon

Question 3

It appears to be because the sides and angles appear to be congruent.

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regular

Question 4

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

180(n – 2)

Question 5

concave✔ convex

Revolt · Accepted Answer

✔ convex

Question 6

How can you best describe a stop sign using polygons?

Revolt · Accepted Answer

8; The sign has sides, so it is .: 8; The sign has sides, so it is .: an octagon; It appears to be because the sides and angles appear to be congruent.: regular

Question 7

x =

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14

Question 8

Complete the statement.

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✔ an octagon; The polygon is and is .: an octagon; The polygon is and is .: convex

Question 9

Complete the statement.

Revolt · Accepted Answer

The polygon is and is .: an octagon; The polygon is and is .: convex

Question 10

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

n – 3; 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 i: n – 3; 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 i: n – 2; 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 i: 180; 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 i: 180(n – 2)

Angle Measures of Polygons Answers

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