Question

Say true or false.

It is possible to have a regular polygon with the measure of each exterior angle as ${22}^0.$

• A. True
• B. False

Answer 1

Answer: (B)

Here, let the number of sides of the polygon be $n.$

So, the number of exterior angles is $n$.

Also, it is a regular one. Therefore, the total number of exterior angles=$n$ and they are equal to each other.

$\therefore$ The sum of the exterior angles = ${360}^o$

$\therefore$ Each angle=$\theta =\frac{{360}^o}{n}⟹n=\frac{{360}^o}{\theta }$ when $nϵN$

i.e $\theta$ should be a complete divisor of ${360}^o.$

Here, $\theta ={22}^o$ which is not a complete divisor of ${360}^o.$

So any regular polygon can not have exterior angle =${22}^o$