Question

How many sides does a regular polygon have if each of its interior angles is 165° Give the answer with a suitable explanation..

Answer 1

Answer:

It's a 24 sided polygon

Step-by-step explanation:

The sum of the measures of the angles of a convex polygon with n sides is (n - 2)180.

The number of interior angles of a polygon equals the number of sides of the polygon.

The sum of all of the angles = 165n

165n = (n - 2)180

165n = 180n - 360

360 = n(180 - 165) = 15n

n = 360/15

n = 24

So it is a 24 sided polygon.