Question

Find the number of sides of a regular polygon that has interior angles of 150 degrees each.

Answer 1

Measure of interior angle = 150°

Number of sides= 180-150  

                           = 30

                          = $\frac{360}{30}$ = 12

Number of sides of the polygon is 12.

Answer 2

First find the exterior angle

So,180°-interior angle (exterior angle property)

180°-150°=30°

Sum of exterior angles =360° (exterior angle property)

hence no•of sides=sum of exterior angle÷each exterior angle

Therefore no •of sides =360°÷30°=12 sides

The polygon has 12 sides