Start with a angle BAC. 

1. Extend either leg (here AC) backwards, away from the interior of the angle. 

2. With the compass at any convenient width, make an arc each side of A, creating points P and Q. 

3. Make the compass width wider, and from P make an arc above A 

4. Repeat from Q, creating the point F above A. 

5. Draw a line from A, up through F 

Done. The angle ∠FAB and the given angle ∠BAC are complementary. (I.E. they add to 90°) 
