Question

(1.) (a.) Is it possible to have a regular polygon with measure of each exterior angle as 22°?
(b.) Can it be an interior angle of a regular polygon? Why?

Answer 1

(a) Since number of sides of a polygon = 360°/each exterior angle
Hence, number of sides of given polygon = 360°/22° = 16.36

Since answer is not a whole number, thus, a regular polygon with a measure of each exterior angle as 22⁰ is not possible.

(b) Here, each interior angle = 22°
Hence, each exterior angle = 180° - 22° = 158°
Hence, number of sides = 360°/158° = 2.27

Since the answer is not a whole number, thus, a regular polygon with a measure of each interior angle as 22⁰ is not possible.