Question

If an interior angle of a regular polygon is 108 degree then find the number of the sides

Answer 1

Let the polygon be x sided.
180 (x-2)/x=108
=180x-360=108x
=180x-108x=360
=72x=360
=x=360/72
=x=5

Answer 2

If the interior angle of a regular polygon is 108 degree then using the formula, we get: [180 x (n-2)] / n where n is the number of sides.

180 x (n-2) / n = 108; 180 n - 360 = 108 n. 180 n - 108 n = 360; 72 n = 360; n= 5; Therefor it is a pentagon.( Having 5 sides)