Start with a angle BAC that we will copy. 

1. Make a point P that will be the vertex of the new angle. 

2. From P, draw a
ray PQ.
This will become one side of the new angle.
 This ray can go off in any direction.
 It does not have to be parallel to anything else.
 It does not have to be the same length as AC or AB.


3. Place the compasses on point A, set to any convenient width. 

4. Draw an arc across both sides of the angle, creating the points J and K as shown. 

5. Without changing the compasses' width,
place the compasses' point on P and draw a similar arc there, creating point M as shown. 

6. Set the compasses on K and adjust its width to point J. 

7. Without changing the compasses' width,
move the compasses to M and draw an arc across the first one, creating point L where they cross. 

8. Draw a
ray
PR from P through L and onwards a little further.
The exact length is not important. 

Done. The angle ∠RPQ is
congruent (equal in measure)
to angle ∠BAC. 
