Question

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

(iv) Duodecagon

Answer 1

General formula for interior angles of regular polygon with n sides $=\left(\frac{n-2}{n}\right)\times {180}^0$

As we know Duodecagon has 12 sides.

So $n=12$

Magnitude of interior angle in degrees

$=\left(\frac{12-2}{12}\right)\times {180}^0={150}^0$

And, magnitude of interior angle in radians

$=\left(\frac{12-2}{12}\right)\times {\pi }^c[\because {180}^0={\pi }^c]$

$={\left(\frac{5\pi }{6}\right)}^c$

Hence, magnitude, in degrees and radians are

${150}^0,{\left(\frac{5\pi }{6}\right)}^c$ respectively.