Construction of 135 Degree Angle with the help of Compass

45 Degree Angle	60 Degree Angle	90 Degree Angle	120 Degree Angle	135 Degree Angle
150 Degree Angle

Before you understand this concept, you are advice to read: What is angle sum property ? 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 at E . (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)