Refer to the diagram and find x in degrees.
My method is to let AB=1, and express AD and AE in terms of AB using sine formula. Then find DE using cosine formula. After that use cosine formula to find cos x. Finally x=20 degrees. However this method relies on the calculator. Is there any PURELY geometric method to solve this problem, such as adding a line which is parallel to line AB, so that it can be PROVEN that x is 20 degrees, without the use of a calculator?