# What is the angle measure of each exterior angle on a 72-sided regular polygon?

Jun 1, 2017

${175}^{\circ}$

#### Explanation:

The formula for the sum of the total measurement of the exterior angles of a polygon is:

$180 - \frac{360}{n}$ where $n =$ the amount of sides on the polygon.

For instance, if we do a regular hexagon, where $n$ would $= 6$, we could use this formula.

$180 - \frac{360}{n}$

$180 - \frac{360}{6} = {120}^{\circ}$

In this instance, $n = 72$

$180 - \frac{360}{n}$

$180 - \frac{360}{72}$

180 - 5 = color(blue)(175^@