Answer:
45 sides
Step-by-step explanation:
we know that
The formula to determine the sum of the interior angles in a regular polygon is
[tex]s=180(n-2)[/tex] ----> 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
[tex]\frac{s}{n}=172[/tex]
[tex]s=172n[/tex] -----> equation B
substitute equation B in equation A and solve for n
[tex]172n=180(n-2)[/tex]
[tex]172n=180n-360[/tex]
[tex]180n-172n=360[/tex]
[tex]8n=360[/tex]
[tex]n=45\ sides[/tex]
