Relatively easy geometry question?

In your diagram, the claim is made that the figure EBCF is supposed to be a square. Using properties of transversals, I can prove that it is a rectangle, i.e. a parallelogram with four right angles. But I don't think the figure is necessarily a square. Consider if the angle at the (exterior) base of the given parallelogram is 40�, so the interior angle is 140�. In this case, the side of the parallelogram and the bisectors will form a right triangle whose acute angles are 70� and 20�. If the rectangle were a square, the angles would have to be 45�. Am I missing something?