Question

(a) Is it possible to have a regular polygon with measure of each exterior angle as ${22}^{\circ }$?
(b) Can it be an interior angle of a regular polygon? Why?

Answer 1

(a)

Exterior angle $={22}^{\circ }$
Let the number of sides $=n$.
In a regular polygon
Sum of the exterior angles $={360}^{\circ }$
$22\times n=360$
$\Rightarrow n=\frac{360}{22}$
$\therefore n=16.36$
Since, $n$ cannot be in decimals as it represents the number of sides of a regular polygon.
Therefore, its not possible to have such polygons.

(b)

Interior angle $={22}^{\circ }$
Exterior angle $=180-22={158}^{\circ }$
Let number of sides $=n$
Since, we have $158\times n=360$
$\Rightarrow n=\frac{360}{158}$
$\therefore n=2.27$
Since, $n$ can't be in decimals as it represents the number of sides of given regular polygon.

Therefore, It is not possible to have such polygon.