Lesson 5.7

- Find Angle Measures in Polygons

What is the angle sum of the triangle?

sides of triangles Angle sum

3

4

5

6

8

180

180

What is the angle sum of the quadrilateral?

Sum 2(180)

sides of triangles Angle sum

3 1 180

4

5

6

8

180

180

What is the angle sum of the pentagon?

Sum 3(180)

sides of triangles Angle sum

3 1 180

4 2 360

5

6

8

180

180

180

What is the angle sum of the hexagon?

Sum 4(180)

sides of triangles Angle sum

3 1 180

4 2 360

5 3 540

6

8

180

180

180

180

What is the angle sum of the octagon?

Sum 6(180)

sides of triangles Angle sum

3 1 180

4 2 360

5 3 540

6 4 720

180

180

180

180

180

180

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Given the angle sum find the number of sides.

- If the measures of the interior angles of a

polygon measures 2700. Classify the polygon by

the number of sides. - Therefore the polygon was a 17 gon.

Example 3 Find an unknown interior angle measure.

- Find the value of x in the diagram.
- The polygon is a quadrilateral.
- Use the corollary to theorem 5.16 Interior angles

of a quadrilateral

Example 4 Find an unknown exterior angle measure.

- Find the value of x in the diagram.
- Use the polygon exterior angles theorem.

Homework 1 6 find the sum of the interior angle

measures of the convex polygon.