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

Jun 5, 2017

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°

Mar 3, 2018

Each interior angle of an 18 sided polygon is $\textcolor{b r o w n}{{160}^{\circ}}$

#### Explanation:

Sum of the interior angles of a polygon is given by the formula

$n \cdot {I}_{18} = \left(2 n - 4\right) \cdot {90}^{\circ} \mathmr{and} = \left(n - 2\right) \cdot {180}^{\circ}$

Since it’s an 18 sided polygon, $n = 18$

Therefore ${\hat{I}}_{18} = \frac{\left(18 - 2\right) \cdot {\cancel{180}}^{\textcolor{b r o w n}{10}}}{\cancel{18}} = \left(16 \cdot 10\right) = {160}^{\circ}$