The steps to draw a triangle with the base BC, a base angle ∠B and the difference of other two sides is given below.
1. Draw the base BC and at point B make an angle say XBC equal to the given angle.
2. Cut the line segment BD equal to AB - AC on the reflection of ray BX (i.e. BX').
3. Join DC and draw the perpendicular bisector, say PQ of DC.
The next step will be:
Let PQ intersect BX at a point A. Join AC.
The next step is:
4. Let PQ intersect BX at a point A. Join AC. Δ ABC is the required triangle. The construction is shown in the image below.