Start with two given angles ∠BAC and ∠RPQ


1. Set the compasses on A and any convenient width. 

2. Make an arc across the angle creating the points J and K. 

3. Move the compasses to point P and make an arc to the right of RP, crossing RP at
the new point L. 

4. Set the compasses' width to the distance JK 

5. Without changing the compasses, set them on point L and make an arc across the previous arc, creating point M 

6. Draw a line from P through M and on to new point S. 

Done. The angle ∠SPQ is the difference between the angles ∠RPQ and ∠BAC. 
