Find the number of sides of a regular polygon whose interior angle is twice the exterior angle.

Find the number of sides of a regular polygon whose interior angle is twice the exterior angle.

Answer Details

Let the ext. angle = x
Thus int. angle = 2x
But sum of int + ext = 180 (angle of a straight line).
2x + x = 180
3x = 180
x = 180/3 = 60
Each ext angle = 360/n
=> 60 = 360/n
n = 360/60 = 6