In quadrilateral $ABCD$, $AD$ is parallel to $BC$ and $AB= AC$ . $F$ is a point on $BC$ such that $DF$ is perpendicular to $BC$. $AC$ intersects $DF$ at $E$. If $BE= 2DF$ and $BE$ bisects $\angle ABC$, find the measure, in degrees, of $∠BAD$ .
I worked out that $\angle ABC = \angle ACB =\angle DAE$
I think the angle bisector theorem could be used but im not sure how to use it in a way that would incorporate the fact that $BE=2DF$