Geometry Problem I've been stuck on

If AEB similar to DEC, then angle  EDC  = angle EAB  and angle ECD = angle EBA

Then  the lines  through AB and CD are parallel because transversals DA and CB form equal opposite interor angles

Angles ECD + EDC  = 180 - angle CED =    180 - 80  =  100    

The supplemental angle to CDB =  111     call this angle D'

The suppplemental angle to ACD =  114     call this angle C'

So

C' + x + ECD  + EDC  + y + D'  =  360

C' + D' + ( ECD + EDC)  + x + y =  360

114 + 111 + (100) + x + y   =  360

325 + x + y =  360

x + y =  360 - 325  =   35