Question

Each interior angle of a regular polygon is double of its exterior angle. Find the number of sides in the polygon.

Answer 1

Let the number of sides in the polygon is $n$

Let the measure of exterior angles be $x$ respectively.

$\Rightarrow$ measure of interior angle $=2x$

$\therefore n\times 2x=(2n-4)\times 90°$

$\Rightarrow nx=(n-2)\times 90°.....\left(i\right)$

Again, we know that,

$nx=360°$

$(n-2)\times 90°=360°\left[\text{From}\left(i\right)\right]$

$n-2=4$

$\Rightarrow n=6$

Hence the number of sides in the polygon are $6$.