Question

How many sides does a regular polygon have if each of its interior angles

is 165°? ​

Answer 1

given one interior angle is 165

we know that measure of each interior angle of a regular polygon is given by the equaltion 180(n-2)/n

where n is the number of sides

since measure of interior angles are 165

165 = 180(n-2)/n

165n=180(n-2)

165n=180n-360

360 = 180n-165n

360=15n

  n  = 360/15

   n  = 24

hence the polygon is 24 sided.