1. Sorry to spoil the party guys, but ^BDC does not equal 70, it is in fact 100.
2. It follows that ^CED is not 70, it is in fact 40.
3. However, the more fundamental error lies when leaving out ^CEF in saying "^CED and ^FEB are supplementary". That is, ^CED + ^FEB is not equal to 180, the correct equation is ^CED + ^CEF + ^FEB = 180.
4. Thus, the proof is wrong. (Unless I overlooked something really badly, or I somehow have a different diagram to everyone else's...)