# Each exterior angle of a regular polygon measures 20. How many sides does the polygon have?

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#### Explanation

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#### Explanation:

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27
Dec 13, 2016

$18$ sides

#### Explanation:

A very useful property to know of any polygon, whether regular or irregular, is that the sum of the exterior angles is always 360°.

For a regular polygon, the size of each exterior angle, $\theta$ can be found from:

theta = (360°)/n" "larr where n = number of sides

Using this property, if you know the size of the exterior angle, you can find the number of sides.

n = (360°)/(20°)

$= 18$ sides

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