If the measure of each interior angle of a regular polygon is 171, what is the number of sides in the polygon?

The polygon will have 40 sides.

The measure of the interior angles of a polygon is determined by the formula

##((n - 2)180)/n## = interior angle measure

were ##n## is the number of angles and sides of the polygon.

We know that the interior angles of the polygon in the question have measures of ##171^o##

##((n - 2)180)/n = 171^o## ##((n - 2)180) = 171^o(n)## ##180n - 360 = 171n## ## -360 = 171n-180n## ##-360 = -9n## ##-360/-9 = n## ##40 = n##

The polygon will have 40 sides.