Question

how to make 135 degree angle by using the compass

Answer 1

Cirst make a 120 degree angle and then make a 150 degree angle then bisect the angles

Answer 2

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 .And with X as center , draw an arc which cuts first arc at D .

4). Again use compass and opened to the same radius .And with D as center , draw another arc which cuts first arc at C .

5). Again use compass and opened to the same radius.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.

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 centerand, 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 = 9O

Now observe the above diagram: 
Angle ZOA + Angle AOE = Angle ZOE

From Statement 1 and 2, we get: 
Angle ZOE = 135