# How much degrees does a pentagon have?

The sum of interior angles is $180 \times 3 = {540}^{o}$ and each angle of a regular pentagon is $\frac{540}{5} = {108}^{o}$

#### Explanation:

There is a cool way to view this (the link below has a complete description):

We know that the sum of the interior angles of a triangle is ${180}^{o}$.

A rectangle can be divided into 2 triangles, each of which have interior angles equaling ${180}^{o}$, and so $2 \times 180 = {360}^{o}$ and that is the sum of the interior angles of a rectangle.

Each angle is $\frac{360}{4} = {90}^{o}$

And we can do the same type of thing with any polygon. Take for example, the pentagon:

The sum of interior angles is $180 \times 3 = {540}^{o}$ and each angle of a regular pentagon is $\frac{540}{5} = {108}^{o}$

https://www.mathsisfun.com/geometry/interior-angles-polygons.html