Question

A regular polygon has an interior angle of 172 degrees

Find the number of sides of this polygon

Answer 1

45 sides

Explanation:

we know that

The formula to determine the sum of the interior angles in a regular polygon is

`s=180(n-2)` ----> equation A

where

s is the sum of the interior angles

n is the number of sides of polygon

we have that

The sum of the interior angles divided by the number of sides is equal to the measure of one interior angle in a regular polygon

so

`(s)/(n)=172`

`s=172n` -----> equation B

substitute equation B in equation A and solve for n

`172n=180(n-2)`

`172n=180n-360`

`180n-172n=360`

`8n=360`

`n=45\ sides`