Question

Fill in the blanks:

Number of sides	Each exterior angle	Each interior angle
		${135}^{\circ }$

Answer 1

Given: Each interior angle is ${135}^{\circ }$
Let each exterior angle be $x$.
Now, $\text{Each exterior angle}+\text{Each interior angle}={180}^{\circ }$
$\therefore {135}^{\circ }+x={180}^{\circ }$
$x={180}^{\circ }-{135}^{\circ }$
$={45}^{\circ }$
So, each exterior angle is ${45}^{\circ }$
Also, Each exterior angle $=\frac{{360}^{\circ }}{n}$
${45}^{\circ }=\frac{{360}^{\circ }}{n}$
$n=\frac{{360}^{\circ }}{{45}^{\circ }}$
$\therefore n=8$
So, the number of sides is $8$.