# The Exterior Angles of a Polygon (Mathematics Lesson)

# 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:

# How to Find the Exterior Angle of a Regular Polygon

**Question:**What is the exterior angle of a regular hexagon?

A regular hexagon has 6 sides, so

**n**= 6.

Using the formula.

Each angle in a 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° |

Octogon | 360° | 45° |

Nonagon | 360° | 40° |

Decagon | 360° | 36° |

Dodecagon | 360° | 30° |

##### Curriculum

##### Interactive Test

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##### Note

**WHAT IS A POLYGON?**

A polygon is a 2-dimensional shape with straight sides.

# INTERIOR ANGLES

Polygons have interior angles as well as exterior angles.The sum of the interior angles of a polygon is given by the formula:

**AN INTERIOR AND EXTERIOR ANGLE IN A POLYGON ADD UP TO 180°**

An interior and exterior angle in a polygon add up to 180°.

Read more about how the interior and exterior angle of a polygon add up to 180°

# WHAT EXTERIOR ANGLES ARE AND WHAT THEY ARE NOT

The exterior angle is the angle between a side and the extension of the side next to it.The exterior angle of a polygon is not the angle outside of a polygon, between two sides.