AB parallel to CD. So
AE=AD
In Traingle AED, angle AED=angle EDA= let us say
So angle BED = 180 -
Angle EDC=?
In Quadrilateral BEDC,sum all angles=360.
Angle B+Angle C=180.
Angle BED+ Angle EDC=180
By above,Angle EDC=180-(180-)=
Which means that DE bisects ADC