6th Grade Math Textbook, Progress

Angles of Polygons

10-11

An interior angle of a convex polygon is an angle

determined by two consecutive sides of the polygon.

In the figure, 
ABCis an interior angle.

The following table shows how you can find the sum of the interior

angles of a convex polygon by drawing all the diagonals from one vertex.

Interior Angles of a Polygon

Polygon Number of Number of Sum of the Measures of

Sides Triangles Formed the Interior Angles

pentagon

5 5 
 2  3 3 180°540°

hexagon

6 6 
 2  4 4 180°720°

octagon

8 8 
 2  6 6 180°1080°

n-gon n n
 2 (n
2)180°

The sum of the measures of the interior angles of a

convex polygon with nsides is (n
2)180°.

Study these examples.

Find the sum of the measures of

the interior angles of a dodecagon.

A dodecagon has 12 sides. The

sum of the measures of the interior

angles is:

( 12 
2)180°

 10 180°

1800°

In the figure, find m
A.

m
A115°90°90°115°( 5 
2)180°

m
A410°540°

m
A130°

B C

A D

E

C

B

A

D

E 115 ° 115 °

2.2

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