Each interior angle of a polygon is $135°$  the number of sides of a polygon is

Each interior angle of a regular polygon

$=\frac{(n-2){180}^{\circ }}{n}={135}^{\circ }$

${180}^{\circ }n-{360}^{\circ }={135}^{\circ }n$

${180}^{\circ }n-{135}^{\circ }n={360}^{\circ }$

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

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

$n=8$