1. Draw a line segment which will become one side of the angle.
(Skip this step if you are given this line.) The exact length is not important. Label it PQ. P will be the angle's vertex. 

In the next 3 steps we create the
perpendicular bisector of PQ.
See Constructing a perpendicular bisector of a line segment

2. Set the compasses' width to just over half the length of the line segment PQ. 

3. With the compasses' point on P then Q, draw two arcs that cross above and below the line. 

4. Draw a line between the two arc intersections. This is at right angles to PQ and bisects it (divides it in exactly half). 


5. With the compasses' point on the intersection of PQ and the perpendicular just drawn, set the compasses' width to P 

6. Draw an arc across the perpendicular, creating the point C 

7. Draw a line from P through C, and on a little more. The end of this line is point R 

8. Done. The angle ∠QPR has a measure of 45° 
