Question

Find the radian measure of the interior angle of a regular (i) Pentagon (ii) Hexagon (iii) Octagon

Answer 1

Sum of interior angle of a regular polygon is $(n-2)\pi$

so in (i) number of sides of pentagon are $5$ thus $n=5\Rightarrow (5-2)\pi \Rightarrow 3\pi$

Sum of all interior angles is $3\pi$ thus measure of each one is $\frac{3\pi }{5}$

(ii) Hexagon $n=6\Rightarrow (6-2)\pi =4\pi$

Sum of all interior angles is $4\pi$ thus measure of each one is $\frac{4\pi }{5}$

(iii) Octagon $n=8\Rightarrow (8-2)\pi =6\pi$

Sum of all interior angles is $6\pi$ thus measure of each one is $\frac{6\pi }{5}$