Question

find the number of sides of a regular polygon if each of its interior angle is 165 degree

Answer 1

let the no. of side be n
 n*165° = 180°(n-2)     [Sum of interior angles = n*(a single interior angle)]

     165n = 180n - 360

    -15n = -360

      n=24

Answer 2

If interior angle is 165 degrees..

Exterior angle is 180-165=15 degrees

For any polygon the sum of all exterior angles is =180 degrees

The number of sides *exterior angle=360

Let n be number of sides

n*15=360

n=360/15

n=24

Therefore number of sides is 24