Question

One exterior angle of regular polygon measures ${10}^o$ What is the measures of each interior angle? How many sides does the polygon have?

Answer 1

The interior angles of teh regular polygon would each have a measure of ${170}^o$ The polygone would have $36$ sides.

Explanation:

The interior and exterior angles of a olygov from a linear pair and are therefore supplementary with a sum of ${180}^o$?

If the exterior angle of polygon is ${10}^o$ then the interior angle must be ${170}^o$.

In order to find the value of teh interior angles of a regular polygon the equation is $\frac{(n-2)180}{n}$ where $n$ is teh number of sides of the regular polygon.

Given that the interior angle is ${170}^o$ we can plug in the value into the formula $170=\frac{(n-2)180}{n}$

$1701n=180n-360$

$-10n=-360$

$n=36$

Therefore teh polygon has $36$ sides.