Draw using a compass and ruler $ 135^{\circ} $ at $ C $ in the line segment CD

2). Now use the compass and open it to any convenient radius. And with C as a center, draw an arc which cuts line segment CD at X. 

3). Again use the compass and opened to the same radius and with X as a center, draw an arc which cuts the first arc at A. 

4). Again use the compass and opened to the same radius and with A as a center, draw another arc which cuts the first arc at B. 

5). Again use the compass and opened to the same radius and with A & B as centers, draw two arcs which cut each other at E. 

6). Join CE and extend it to F. 

7). Above formed angle, FCD = 90 Degrees. 

8). Extend DC to Z. 

9). Since ZD is a straight line, so formed Angle FCZ = 90 Degrees.

10). Again use the compass and open it to any convenient radius and with C as the center, draw an arc which cuts line segment CD at P and CF at Q. 

11). Again use the compass and opened to the same radius (as of step 10) and with P & Q as centers and draw two arcs that cut each other at a point G. 

12). Join CG and extend it to H. 

13). HC is the bisector of angle FCD. 

Therefore, Angle FCH = Angle HCD = ½ of Angle FCD = 45 Degree each 

14). Now observe that: 

Angle ZCF = 90

Angle FCH = 45

Add both the angles and we get 

Angle ZCF + Angle FCH = 9O + 45 = Angle ZCH 

So Angle ZCH = 135 degrees