Question

State true or false.

Is it possible to have a regular polygon whose each exterior angle is $\frac{1}{8}$ of a right angle.

• A. True
• B. False

Answer 1

The correct option is A True

Given, a regular polygon whose each exterior angle is $\frac{1}{8}$ of a right angle$=$ $\frac{1}{8}\times {90}^o$

$=\frac{{45}^o}{4}$
Each exterior angle of a regular polygon $=$ $\frac{{360}^o}{n}$, where n $=$ number of sides
Now,
$\frac{{360}^o}{n}=\frac{{45}^o}{4}$
Hence , $n=8$
Since, $n$ should be an integer, so their exist a regular polygon whose each exterior angle is $\frac{1}{8}$ of a right angle.