Question

How many sides does a polygon have if the sum of the interior angles is ${1440}^o$

Answer 1

Since sum of the interior angles is ${1440}^0$, therefore, $(2n–4){90}^0={1440}^0$

$2n–4=\frac{1440}{90}\Rightarrow 2n–4=16\Rightarrow 2n=16+4\Rightarrow 2n=20\Rightarrow n=\frac{20}{2}=10$

Hence, the polygon has $10$ sides.