Question

Express in radians and also in degrees the angle of a regular polygon of (i) $40$ sides (ii) $n$ sides.

Answer 1

We know that

$\left(ii\right)$ Each angle of a regular polygon of $n$ sides

In radian $=\left(\frac{n-2}{n}\right)\pi$

In Degree $=\left(\frac{n-2}{n}\right)\times {180}^0$

$\left(i\right)$. Each angle of regular polygon on $n=40$ sides

In radian $=\left(\frac{n-2}{n}\right)\pi$

$=\left(\frac{40-2}{40}\right)\pi$

$=\frac{38\pi }{40}=\frac{19\pi }{20}$ rad

In Degree $=\left(\frac{n-2}{n}\right)\times {180}^o$

$=\left(\frac{40-2}{40}\right)\times {180}^o$

$=\frac{38}{40}\times {180}^o$

$=\frac{38}{2}\times 9^o$

$=19\times 9$

$={171}^o$