Construction of 45 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

To construct 45 degree angle, first we draw 90 degree angle and its done in the following steps: 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 arcs 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 Now, to construct at 45 degree angle, we will construct the angle bisector of above angle AOB. And its done in the following steps: 8). 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) 9) Again use compass and opened to same radius (as of step 8).And with P & Q as center and, draw two arcs which cuts each other at point F. (as shown below) 10) Join OF and extend to E. (as shown below) 11) EO is the bisector of Angle AOB Therefore, Angle AOE = Angle EOB = ½ of Angle AOB = 45 Degree each (as shown below)