Exterior Angles of a Polygon

In a polygon, an exterior angle is formed by a side and an extension of an adjacent side.

** The sum of the exterior angles of any polygon is 360º **

The **measure the one exterior angle** of an equangular polygon can be calculated by using the following table:

Number of sides |
Measure of 1 exterior angle |
Sum of exterior angles |

3 |
120º |
3·120º=360º |

4 |
90º |
4·90º=360ª |

5 |
72º |
5·72º=360º |

... |
... |
... |

n |
360º/n |
360º |

What is the degree measure of an exterior angle of a regular nonagon?

A nonagon has nine vertices, so divide the measure of the sum of the exterior angles by 9.

360º ÷ 9 = 40º

The degree measure of an exterior angle of a regular nonagon is 40º