Question

Fill in the blanks:​
(v)

Answer 1

Given : Each exterior angle is ${135}^{\circ }$
Let each exterior angle be $x$.

Now, Each $\text{exterior angle}+\text{Each interior angle}={180}^{\circ }$

$\therefore$ ${135}^{\circ }+x={180}^{\circ }$

$x={180}^{\circ }-{135}^{\circ }$

$={45}^{\circ }$
So, each exterior angle is ${45}^{\circ }$

Also , each exterior angle $=\frac{{360}^{\circ }}{n}$

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

$\therefore$ $n=\frac{{360}^{\circ }}{{45}^{\circ }}$

$\therefore$ $n=8$

So ,the number of sides is $8$.