How to construct 135 degree angle with compass and ruler

Hey yar here is ur answer
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.  

 

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 .
 

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 .

 

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
 

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 at E .

 

6). Join OE and extent it to A.  

 

7). Above formed angle AOB = 90 Degree . 

8) . Extend BO to Z .

 

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 .

 

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. () 

 

12). Join OF and extend to E .

 

13). EO is the bisector of Angle AOB. 
Therefore, Angle AOE = Angle EOB = ½ of Angle AOB = 45 Degree each

 

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�