MathNet 2016-part-04 — 184 problems (EN–VI) Question 123

Let $ABCD$ be a convex quadrilateral with $\angle DAB = 90^\circ$. Let $M$ be the midpoint of $BC$. Given that $\angle ADC = \angle BAM$, prove that $\angle ADB = \angle CAM$. (E. Bakaev)