Question

How many sides does a regular polygon have if each of its interior angle is 160 degree

Answer 1

Let the no.of sides in the polygon be n.

Each interior angle of the polygon= 160°

Sum of angles in the polygon= 160n

Also, sum of angles in the polygon= (n - 2)×180°

180(n - 2)= 160n

180n - 360= 160n

180n - 160n= 360

20n= 360

n= 360/20= 18

So the number of sides in the polygon is 18.