# What is the measure of each interior angle of an 18 sided polygon?

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Jan 22, 2018

#### Answer:

The measure of each interior angle of an $18$-sided polygon is ${160}^{\circ}$.

#### Explanation:

First, start with the interior sum formula,

$\left(n - 2\right) \cdot {180}^{\circ}$

The variable $n$ stands for how many sides of the polygon. This is an $18$-sided polygon, so plug in the sides.

$\left(18 - 2\right) \cdot {180}^{\circ} = {2880}^{\circ}$

After you find the sum of the interior angles, just divide the sum by how many sides you have.

${2880}^{\circ} / 18 = {160}^{\circ}$

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#### Answer:

160°

#### Explanation:

An alternative method is to use the exterior angle.

the sum of the exterior angles is ALWAYS 360°

So you can find the size of the exterior angles of a regular polygon quite easily:

If there are $18$ sides $\left(n = 18\right)$, then each exterior angle is:

(360°)/n = (360°)/18 = 20°

The sum of the exterior and interior angles is 180° because they are adjacent angles on a straight line.

$\therefore$ each interior angle is 180° - 20° = 160°

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