IOM 2016 Problem 4

A convex quadrilateral $ABCD$ has right angles at $A$ and $C$ . A point $E$ lies on the extension of the side $AD$ beyond $D$ so that $\angle ABE =\angle ADC$ . The point $K$ is symmetric to the point $C$ with respect to point $A$ . Prove that $\angle ADB =\angle AKE$ .