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# Exterior Angles of a Polygon

(KS2, Year 6)

## The Lesson

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° |

## Beware

## What Exterior Angles Are...

The exterior angle is the angle between a side and the extension of the side next to it.## ...And What Exterior Angles Are Not

The exterior angle of a polygon is not the angle outside of a polygon, between two sides.## 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°

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