# The Exterior Angles of a Polygon

## The Exterior Angles of a Polygon

The exterior angles of a polygon are the angles outside of the polygon, between a side and the extension of the side next to it.

## The Sum of the Exterior Angles of a Polygon

The sum of the exterior angles of a polygon is:

The exterior angles of a polygon add up to 360°, a full revolution.

## The Exterior Angles of a Regular Polygon

Regular polygons have equal exterior angles.

There are as many exterior angles as there are sides.

To find each exterior angle in a regular polygon, divide the sum of the exterior angles by the number of sides.

The formula for each of the exterior angles of a regular polygon is:

### Example

Imagine you wanted to find an interior angle of a regular hexagon.

A regular hexagon has 6 sides, so **n** = 6.

Using the formula:

Exterior angle = 360° ÷ n

Exterior angle = 360° ÷ 6

Exterior angle = 60°

Each angle in a regular hexagon is 60°.

Read more about how to find the exterior angle of a regular polygon

## The Exterior Angles of Different Polygons

Shape | Sum of Exterior Angles | Exterior Angle of Regular Polygon |
---|---|---|

Triangle |
360° | 120° |

Quadrilateral |
360° | 90° |

Pentagon |
360° | 72° |

Hexagon |
360° | 60° |

Heptagon |
360° | 51.4° |

Octagon |
360° | 45° |

Nonagon |
360° | 40° |

Decagon |
360° | 36° |

Dodecagon |
360° | 30° |