In a certain regular polygon, the measure of each interior angle is nine times the measure of each exterior angle. Find the number of sides in this regular polygon.
+128475 Measure of an interior angle = (n-2)(180) / n
Measure of an exterior angle = (360)/n
Where n is the number of sides
So we have that
(9)(360)/n = (n - 2) (180)/n multiply through by n
(9)(360) = (n - 2) (180) simplify
3240 = 180n - 360
3240 + 360 = 180n
[3240 + 360 ] / 180 = n
20 = n
