A pentagon has 5 sides, and can be made from **three triangles**, so you know what ...

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... its interior angles add up to 3 × 180° =** 540° **

And when it is **regular** (all angles the same), then each angle is 540**°** / 5 = 108**°**

(Exercise: make sure each triangle here adds up to 180°, and check that the pentagon"s interior angles add up to 540°)

The Interior Angles of a Pentagon add up to 540°

## The General Rule

Each time we add a side (triangle to quadrilateral, quadrilateral to pentagon, etc), we **add another 180°** to the total:

ShapeSidesSum of

**Interior AnglesShapeEach Angle**

If it is a Regular Polygon (all sides are equal, all angles are equal) | ||||

Triangle | 3 | 180° | 60° | |

Quadrilateral | 4 | 360° | 90° | |

Pentagon | 5 | 540° | 108° | |

Hexagon | 6 | 720° | 120° | |

Heptagon (or Septagon) | 7 | 900° | 128.57...° | |

Octagon | 8 | 1080° | 135° | |

Nonagon | 9 | 1260° | 140° | |

... | ... | .. | ... See more: What Is The Longest Street In The United States ? History Of Colfax Avenue | ... |

Any Polygon | n | (n−2) × 180° | (n−2) × 180° / n |

So the general rule is:

Sum of Interior Angles = (**n**−2) × 180**°**

Each Angle (of a Regular Polygon) = (**n**−2) × 180**°** / **n**

Perhaps an example will help:

### Example: What about a Regular Decagon (10 sides) ?

Sum of Interior Angles = (

**n**−2) × 180

**°**

= (

**10**−2) × 180

**°**

= 8 × 180°

=

**1440°**

And for a Regular Decagon:

Each interior angle = 1440**°**/10 = **144°**

Note: Interior Angles are sometimes called "Internal Angles"

Interior Angles Exterior Angles Degrees (Angle) 2D Shapes Triangles Quadrilaterals Geometry Index