Question

The sum of all interior angles of a regular polygon is ${1080}^{\circ }$. What is the measure of each of its interior angles ?

(a) 135${}^{\circ }$ (b) 120${}^{\circ }$ (c) 156${}^{\circ }$ (d) 144${}^{\circ }$

Answer 1

Sum of all interior angles of polygon = ${1080}^{\circ }$ Let n be the number of sides, then $\therefore$ (2n-4)$\times$ 90${}^{\circ }$ = ${1080}^{\circ }$ 2n-4=$\frac{{1080}^{\circ }}{{90}^{\circ }}$ = 12 2n=12+4=16 $\Rightarrow$ n = $\frac{16}{2}$ = 8 $\therefore$ Each angle = $\frac{1080}{8}={135}^{\circ }$