I suspect that the original problem should have been AE=ED=DB=BC. Then there would be a very nice proof that the ratio of angles A & B is 1:3. You would use Isosceles Triangle thm and Exterior Angle of Triangle thm.
In order to draw such a diagram, angle A needs to be more acute than the one on the original diagram. (If AB=AC than angle A would be exactly 180/7.)