Question

Find the magnitude, in radians and degrees, of the interior angle of a regular

$\left(ii\right)$ Octagon

Answer 1

General formula for interior angles of regular polygon with $n$ sides

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

As we know Octagon has $8$ sides, so $n=8$

Magnitude of interior angle in degrees

$=\left(\frac{8-2}{8}\right)\times {180}^{\circ }$

$={135}^{\circ }$

And, magnitude of interior angle in radians

$=\left(\frac{8-2}{8}\right)\times {\pi }^c$

$[\because {180}^{\circ }={\pi }^c]$

$={\left(\frac{3\pi }{4}\right)}^c$

Hence, magnitude, in degrees and radians are ${135}^{\circ },{\left(\frac{3\pi }{4}\right)}^c$ respectively.