Question

How many sides does a polygon have if the difference between its interior and exterior angle of the polygon is 180° ?​

Answer 1

hi dear

Let the interior angle and exterior angle of the regular polygon be x° and y° respectively. We know that their sum is 180°. So x+y= 180…..(1) Also given that the difference between the interior angle and exterior angle = 120°. Hence, x-y=120°………(2)

Subtracting (2) from (1) we have 2y = 60° or y=30°. Hence each exterior angle = 30°. Therefore the number of sides =360/ ext angle = 360/30 = 12.

So the regular polygon has 12 sides.

hopes its helps you