Question

The number of sides of a regular polygon whose each interior angle is ${135}^{\circ }$

Answer 1

The sum of the exterior angles of any polygon is ${360}^{\circ }$
If an interior of the given regular polygon is ${135}^{\circ }$.

then, the corresponding exterior is $180-135={45}^{\circ }$
So each of the exteriors is ${45}^{\circ }$
Number of exterior angles $=\frac{360}{45}=8$
Number of sides $=$ number of exterior angles $=8$