CK-12 Geometry Concepts

6.2. Exterior Angles in Convex Polygons http://www.ck12.org

MEDIA

Click image to the left for more content.

CK-12 Foundation: Chapter6ExteriorAnglesinConvexPolygonsB

Concept Problem Revisited

The exterior angles of a regular polygon sum to 360◦. The measure of each exterior angle in a dodecagon (twelve-
sided regular polygon) is^360
◦
12 =^30

◦.

Vocabulary

Anexterior angleis an angle that is formed by extending a side of the polygon. Aregularpolygon is a polygon in
which all of its sides and all of its angles are congruent.

Guided Practice

Find the measure of each exterior angle for each regular polygon below:

1. 12-gon


2. 100-gon


3. 36-gon

Answers:

For each, divide 360◦by the given number of sides.

1. 30◦


2. 
   
   
   
   3. 6 ◦
   
   
   
   


3. 10◦

Practice

1. What is the measure of each exterior angle of a regular decagon?


2. What is the measure of each exterior angle of a regular 30-gon?


3. What is the sum of the exterior angles of a regular 27-gon?

Find the measure of the missing variables:

4.

5.

6. The exterior angles of a quadrilateral arex◦, 2 x◦, 3 x◦,and 4x◦.What isx?

Find the measure of each exterior angle for each regular polygon below:

7. octagon