<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
Dismiss
Skip Navigation
Our Terms of Use (click here to view) have changed. By continuing to use this site, you are agreeing to our new Terms of Use.

Exterior Angles in Convex Polygons

Angles on the outside of a polygon formed by extending a side.

Atoms Practice
Estimated6 minsto complete
%
Progress
Practice Exterior Angles in Convex Polygons
Practice
Progress
Estimated6 minsto complete
%
Practice Now
Turn In
Exterior Angles in Convex Polygons

Exterior Angle Sum Theorem

An exterior angle is an angle that is formed by extending a side of the polygon.

As you can see, there are two sets of exterior angles for any vertex on a polygon, one going around clockwise ( hexagon), and the other going around counter-clockwise ( hexagon). The angles with the same colors are vertical and congruent.

The Exterior Angle Sum Theorem states that the sum of the exterior angles of ANY convex polygon is . If the polygon is regular with sides, this means that each exterior angle is .

What if you were given a seven-sided regular polygon? How could you determine the measure of each of its exterior angles?

 

 

Examples

Example 1

What is the measure of each exterior angle of a regular 12-gon?

Divide  by the given number of sides.

Example 2

What is the measure of each exterior angle of a regular 100-gon?

Divide  by the given number of sides.

Example 3

What is ?

is an exterior angle and all the given angles add up to . Set up an equation.

Example 4

What is the measure of each exterior angle of a regular heptagon?

Because the polygon is regular, the interior angles are equal. It also means the exterior angles are equal.

Example 5

What is the sum of the exterior angles in a regular 15-gon?

The sum of the exterior angles in any convex polygon, including a regular 15-gon, is .

Review

  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:

  1. The exterior angles of a quadrilateral are and What is ?

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

  1. octagon
  2. nonagon
  3. triangle
  4. pentagon

Review (Answers)

To see the Review answers, open this PDF file and look for section 6.2. 

Resources

 

Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes
Please to create your own Highlights / Notes
Show More

Vocabulary

exterior angle

An angle that is formed by extending a side of the polygon.

regular polygon

A polygon in which all of its sides and all of its angles are congruent.

Exterior Angle Sum Theorem

Exterior Angle Sum Theorem states that the exterior angles of any polygon will always add up to 360 degrees.

Image Attributions

Explore More

Sign in to explore more, including practice questions and solutions for Exterior Angles in Convex Polygons.
Please wait...
Please wait...