Answer:
[tex]AE=EC[/tex]
[tex]\angle ADB \cong \angle CBD[/tex]
[tex]m\angle ADC + m\angle DCB = 180\°[/tex]
Step-by-step explanation:
In the given parallelogram, we know that
[tex]AD \parallel BC\\AB \parallel DC[/tex]
From this parallels and having segment [tex]DB[/tex] as a transversal, we have
[tex]\angle ADB \cong \angle CBD[/tex] by alternate interior angles.
Then, we have
[tex]AE=EC[/tex] by givens.
Finally, we have
[tex]m\angle ADC + m\angle DCB = 180\°[/tex] , by consecutive interior angles, which are supplementary by definition.
Therefore, the right answers are
[tex]AE=EC[/tex]
[tex]\angle ADB \cong \angle CBD[/tex]
[tex]m\angle ADC + m\angle DCB = 180\°[/tex]
