## Angles of Polygons

To find the sum of angles in a polygon, you can simply use the following formula:

where *n* is the number of sides

For example, a triangle has three sides therefore the total sum of angles is:

How about a 4-sided polygon (also called quadrilaterals)?

This could go on and on...

In fact, a table could be made here...

Polygon |
Sides |
Sum of Angles |

Triangle | 3 | 180° |

Quadrilateral | 4 | 360° |

Pentagon | 5 | 540° |

Hexagon | 6 | 720° |

Heptagon | 7 | 900° |

Octagon | 8 | 1080° |

Nonagon | 9 | 1260° |

Decagon | 10 | 1440° |

...of course, the number of polygons does not stop here. However, there is an ever increasing pattern of 180° per one side added.

In addition, for any regular polygon, dividing the sum of angles by the number of sides (or vertices) would result in the angle of each vertex. A *regular polygon* is a *polygon* that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length). *Regular polygons* may be convex or concave.

### Examples:

1. Find the sum of angles of a regular polygon that has 15 sides (pentadecagon):

### Show Answer

Use the sum of angles formula:

2. Find the angle on a vertex of a regular pentadecagon:

### Show Answer

Since the sum of angles is 2340°, then