fbpx

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.