Given the angles and diagonals of a quadrilateral, construct the quadrilateral using only a straightedge, a pencil, and a compass

Question

I tried to do this by constructing 1 angle, and then constructing 2 circles with their radii equal to the diagonals with their centres on the vertex of the angle, but I couldn't get any further from there.

This is one of the Jewish problems from the Moscow State University, but I couldn't find a solution online.