MathNet 2019-part-02 — 184 problems (EN–VI) Question 140

Let $A$, $B$, $C$ and $D$ be points on a circle such that $|AB| = |BC| = |CD|$. The angle bisectors of $\angle ABD$ and $\angle ACD$ intersect at the point $E$.
If the lines $AE$ and $CD$ are parallel, find $\angle ABC$.
(Matko Ljulj)