# The measure of an interior angle of a regular polygon is 160. How many sides does the polygon have?

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sjc Share
Jul 9, 2017

$18 \text{ sides }$

#### Explanation:

with regular polygons it is best to remember that:

$\left(1\right) \text{ }$all the EXTERIOR angles add up to ${360}^{0}$

$\left(2\right) \text{ }$ $1 \text{ exterior angle"+ 1" interior angle } = {180}^{0}$

Work with the exterior angles. In this case:

$1 \text{ int. <} = 180 - 160 = {20}^{0}$

$\text{No. of sides } = \frac{360}{20} = 18$

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