Question

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

$\left(i\right)$ Pentagon

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 Pentagon has $5$ sides, so $n=5$

Magnitude of interior angle in degrees

$=\left(\frac{5-2}{5}\right)\times {180}^{\circ }$

$={108}^{\circ }$

And, magnitude of interior angle in radians

$=\left(\frac{5-2}{5}\right)\times {\pi }^c$

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

$={\left(\frac{3\pi }{5}\right)}^c$

Hence, magnitude, in degrees and radians are ${108}^{\circ },{\left(\frac{3\pi }{5}\right)}^c$ respectively.