Given two angles ∠A=x∘,∠B=y∘ and AB;(A+B<90∘), how many triangles can be constructed?
One
Draw AB, at point A draw a ray making angle x∘ with AB, and at point B draw a ray making y∘ with BA, such that the two rays intersect at a point forming a triangle. Therefore only one triangle can be formed with the given data.