I will not answer this (I've got no time) but I will point these out:

1) angleAEB is a vertical angle to CED

2) angle ABE = 180 - angleCDE

3) angle EAB = 180 - angle ECD

4) angle BAD = 180 - angle ADC

5) angle BCD = 180 - angle ABC

6) angle AED + angle BEC = 360 - ( angle AEB + angle CED )