Question

Question 49
The number of sides of a regular polygon in which each interior angle measures ${135}^{\circ }$ is
a) 6
b) 7
c) 8
d) 9

Answer 1

We know that, the measure of each exterior angle of a polygon having n sides is given by $\frac{{360}^{\circ }}{n}$.

$\therefore$ The number of sides,
$n=\frac{{360}^{\circ }}{Exteriorangle}=\frac{{360}^{\circ }}{{180}^{\circ }-{135}^{\circ }}$

[$\because$ exterior angle + interior angle $={180}^{\circ }$]

$=\frac{{360}^{\circ }}{{45}^{\circ }}=8$