Question

Each interior angle of a regular polygon is 150°. how many sides has the polygon​

Answer 1

Given parameters:

Each interior angle  = 150°

Unknown:

The number of sides of this regular polygon = ?

Solution:

To find the sum of internal angles of a regular polygon, we use the expression below;

              (n - 2) x 180  = sum of internal angles of a polygon

n is the number of sides,

   Also, the sum of the internal angles of a polygon = number of sides x internal angles;

 So;

            (n-2) x 180 = 150 x n

 Solve for n;

           180n - 360 = 150n

           180n - 150n  = 360

                30n  = 360

                n = 12;

Therefore, the number of sides is 12