Question

Question 40
Which of the following can never be the measure of the exterior angle of a regular polygon?
a) ${22}^{\circ }$
b) ${36}^{\circ }$
c) ${45}^{\circ }$
d) ${30}^{\circ }$

Answer 1

We know that the sum of all exterior angles of a polygon is ${360}^{\circ }$.
The measure of each exterior angle is $\frac{{360}^{\circ }}{n}$, where n is the number of sides/angles.
Thus, the measure of each exterior angle will always be a factor of ${360}^{\circ }$.
Hence, ${22}^{\circ }$ can never be the measure of the exterior angle of a regular polygon.