Question

The measure of the external angle of a regular octagon is

• A. $\pi /4$
• B. $\pi /6$
• C. $\pi /8$
• D. $\pi /12$

Answer 1

The correct option is A $\pi /4$

$\Rightarrow$ The sum of the exterior angles of regular octagon is ${360}^o$.

$\Rightarrow$ Number of sides of octagon $=8$

$\Rightarrow$ The measure of the external angles $=\frac{{360}^o}{8}={45}^o$

In radian $={45}^o\times \frac{\pi }{{180}^o}=\frac{\pi }{4}$

$\therefore$ The measure of the external angle of a regular octagon is $\frac{\pi }{4}$