KöMaL 2015 C1317

The interior angles lying at vertices $A$ , $B$ , $C$ and $D$ of a pentagon $ABCDE$ are $90^\circ$, $60^\circ$, $150^\circ$ and $150^\circ$, respectively. Furthermore $AB=2BC=\frac 43 AD$ . Prove that the line segment joining the intersection of lines $AE$ and $CD$ to the intersection of lines $AD$ and $BC$ is parallel to $AB$ .