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

Correct option is (a).

We know that sum of interior angles of a $n$ sided polygon is $(n-2)\times {180}^{\circ }$

$\therefore (n-2)\times {180}^{\circ }={1080}^{\circ }$

$\Rightarrow (n-2)=10$

$\Rightarrow n=8$

Therefore, measure of each interior angle $=\frac{\text{Sum of all the angles}}{\text{Total no. of sides}}$

$=\frac{{1080}^{\circ }}{8}$

$={135}^{\circ }$