Question

THE EXTERIOR ANGLE OF A REGULAR POLYGON IS ONE FIFTH OF ITS INTERIOR ANGLE , FIND THE NUMBER OF SIDES IN THE POLYGON?

Answer 1

Let the interior angle be x 
exterior angle would be 1/5(x)
we know that sum of interior and exterior angles should be equal to 180 degrees
x+ x/5 = 180
6x/5 = 180
6x = 900
x = 900/6 
x =150
we know that sum of interior angles of a polygon is (n-2)x180 where n is number of sides
(n-2)x180 = 150xn  ie, sum of all angles
180n - 360 = 150n
30n = 360
hence n = 360/30
which is equal to 12
polygon has 12 sides