I've got it narrowed down to a set of 4 linear equations in 4 unknowns which (unfortunately) don't seem to nonsingular. But it appears to be a tighter constraint than 0° < x < 130°

I have:
<CDE + <DEC = 160&deg; <DEC + <AED = 150&deg; <AED + <EDB = 130&deg; <EDB + <CDE = 140&deg; At this point, I realized that there must be some relationship, probably involving triangle ACB being isosceles, that I'm unaware of. The next rabbit hole I'm tempted to run down involved bisecting <DBE to get point F, with FE parallel to BA, and see if that gives me any more promising relationships. It does... It gives me an upper bound x < 70&deg;