Question

A regular polygon has each interior angle is 156°, what is the number of sides of the polygon? A. 14 C. 16 B. 15 D. 17​

Answer 1

option B. 15

Explanation:

Sum of interior angles of a polygon with n sides = ( n - 2 ) x 180°

Therefore each interior angle,

`(n - 2)/(n) * 180^\circ`

Given the interior angles = 156°

That is ,

`((n-2)/(n)) * 180 = 156\\\\(n-2)/(n) = (156)/(180)\\\\1- (2)/(n) = (156)/(180)\\\\1 - (156)/(180) = (2)/(n)\\\\(180-156)/(180) = (2)/(n)\\\\(24)/(180) = (2)/(n)\\\\24 * n = 2 * 180\\\\n = (2 * 180)/(24) =(180)/(12) = 15`

Answer 2

option B is correct

interior angle of given polygon =156

exterior angle of polygon=180 - 156 =24

as we know that sum of exterior angle of any polygon is 360 degree

so number of sides of regular polygon=360/24=15