# What is the sum of the measures, in degrees, of the interior angles of a 20-sided polygon?

May 19, 2018

All enclosed polygons have an internal angle measure of either ${180}^{o}$ for triangles and ${360}^{o}$ for polygons of 4 sides or more.

#### Explanation:

The internal angle measure of a triangle no matter the type is ${180}^{o}$

The 4 sided polygons (square being the most understood) has an interior angle measure of 4 x ${90}^{o}$ or ${360}^{o}$

for an equilateral 20 sided polygon the equation is ${360}^{o} / \text{20}$= ${18}^{o}$

if the sides are of varying length then the polygon has to be plotted and the answer is more complex as the adjacent side lengths have to be taken into account.

May 19, 2018

The sum is 3240˚.

#### Explanation:

The formula for calculating the sum of the interior angles of a polygon is as follows:

$\left(n - 2\right) \cdot 180$

$n$ is the number of sides of the polygon.

In this case, we can plug in $20$ to get the following:

$\left(20 - 2\right) \cdot 180$

$18 \cdot 180$

$3 , 240$