### Regular Polygons

Regular polygons have all sides, and all angles equal.

Size of Internal Angles

To find the size of the internal angles of a regular polygon with ‘n’ sides, use the formula:

For example, the size of the interior angles of the pentagon (five sides) above is:

The sum of all the interior angles of a polygon with ‘n’ sides is found using the formula:

(n – 2) x 180°

Therefore, the sum of all the interior angles of the pentagon above is:

(5 – 2) x 180° = 3 x 180° = 540°

Size of Exterior Angles

Interior and Exterior angles are measured on the same line, that is, they add up to 180°.

Therefore, the size of an exterior angle = 180° – Interior angle.

For example, the size of the external angle of the pentagon above is:

Since, interior angle = 108°

Then, exterior angle = 180° – Interior angle

180° – 108° = 72°

Below is a list of the names and the number of sides, of some of the most popular polygons.

Name of Polygon |
Number of Sides |

Equilateral Triangle | 3 |

Quadrilateral | 4 |

Pentagon | 5 |

Hexagon | 6 |

Heptagon | 7 |

Octagon | 8 |

Nonagon | 9 |

Decagon | 10 |