We are told that the measure of an interior angle of a regular n -sided convex polygon is about 166.15, and want to find the number of sides n of the polygon. Keep in mind that all the angles in a regular polygon are congruent. Therefore, the sum of their measures is equal to 166.15 multiplied by n.
166.15nThe Polygon Interior Angles Sum Theorem tells us that the sum of the measures of the interior angles of an n-sided convex polygon is (n-2)180. We know that it is equal to 166.15n.
(n-2)180 = 166.15n
Let's solve this equation to find n.
