Question

Find the radian measure of the interior angles of a regular polygon of 12 sides.

Answer 1

We know that, for an n-sided polygon, the sum of all interior angles is $(n-2)\times {180}^o$

Therefore, for a regular polygon, the measure of each interior angle is $\frac{\left(n-2\right)\times {180}^o}{n}$

Given that, the regular polygon has 12 sides.

$\therefore \frac{\left(12-2\right){180}^o}{12}$

$\Rightarrow \frac{10\times {180}^o}{12}$

$\Rightarrow \left(\frac{5\times {180}^o}{6}\right)={150}^o$

$\therefore$ Each angle in radian$={150}^o\times \frac{\pi }{180}=\frac{5\pi }{6}$

Hence, the radian measure of the interior angles of a regular polygon of 12 sides is $\frac{5\pi }{6}$