Saccheri Quadrilateral

Girolamo Saccheri (1677-1733) was an Italian mathematician who for many years tried to prove the fifth Euclidean axiom from the other four.  He based his proof attempts on the idea of negation. If he assumed Euclid 1-4 as axioms and assumed the opposite of Euclid 5 and then reach a contradiction to something known to be true, then the opposite of Euclid 5 could not hold simultaneously with the first 4 axioms, and thus Euclid 5 must be true as a consequence of the other four axioms.

One of his proof attempts involved the construction of a quadrilateral ABCD in which the sides AD and BC are assumed equal and there are right angles at points A and B.  To construct this figure:

 
The Saccheri Quadrilateral has some interesting properties. One of these is shown. If we measure the two upper angles, these appear to be always congruent, but never 90 degrees! Can you prove this?