My Favorite Math Problem

Using only elementary geometry, determine angle x. Provide a step-by-step proof.

You may use only elementary geometry, such as the fact that the angles of a triangle add up to 180 degrees and the basic congruent triangle rules (side-angle-side, etc.). You may not use trigonomery, such as sines and cosines, the law of sines, the law of cosines, etc. 

This is the hardest problem I have ever seen that is, in a sense, easy. It really can be done using only elementary geometry. This is not a trick question.  (K. Enevoldsen)