How to draw 135°

To construct 135 degree angle we first construct 90 degree angle and its steps of constructions are as follows:  1). Use ruler and draw a Line segment OB of any convenient length. (as shown below)   2). Now use compass and open it to any convenient radius. And with O as center , draw an arc which cuts line segment OB at X . (as shown below)   3). Again use compass and opened to the same radius (as of step 2). And with X as center , draw an arc which cuts first arc at D . (as shown below)   4). Again use compass and opened to the same radius (as of step 2). And with D as center , draw another arc which cuts first arc at C . (as shown below)   5). Again use compass and opened to the same radius (as of step 2). And With C & D as center, draw two arc which cuts each other atE . (as shown below)   6). Join OE and extent it to A. (as shown below)   7). Above formed angle AOB = 90 Degree .  8) . Extend BO to Z . (as shown below)   9). Since ZB is a straight line, so formed Angle AOZ = 90 Degree (angle sum property)   Now, to construct at 135 degree angle, we will construct the angle bisector of above angle AOB. And its done in the following steps:  10). Again use compass and open it to any convenient radius. And with O as center , draw an arc which cuts line segment OB at P and OA at Q . (as shown below)   11). Again use compass and opened to same radius (as of step 10).And with P & Q as center and, draw two arcs which cuts each other at point F. (as shown below)   12). Join OF and extend to E . (as shown below)   13). EO is the bisector of Angle AOB.  Therefore, Angle AOE = Angle EOB = ½ of Angle AOB = 45 Degree each (as shown below)   14). Now observe that:  Angle ZOA = 90°  Angle AOE = 45°  Add both the angles and we get  Angle ZOA + Angle AOE = 90° + 45° ..... (Statement 1)  Now observe the above diagram:  Angle ZOA + Angle AOE = Angle ZOE ..... (Statement 2)  From Statement 1 and 2, we get:  Angle ZOE = 135° (as highlighted with pink color)  

The steps of constructions are: 

(a) Draw a line PQ and take a point O on it.

(b) Taking O as the centre and convenient radius, mark an arc, which intersects PQ at A and B.

(c) Taking A and B as centres and radius more than half of AB, draw two arcs intersecting each other at R.

(d) Join OR. Thus, ∠QOR = ∠POQ = 90 .

(e) Draw OD the bisector of ∠POR. Thus, ∠QOD is the required angle of 135.

(f) Now, draw OE as the bisector of ∠QOD=1/2 of 135=67.5