Let $ABCD$ be a convex quadrilateral with $\angle BCD= 120^o, \angle {CBA} = 45^o, \angle {CBD} = 15^o$ and $\angle {CAB} = 90^o$. Show that $AB = AD$.
Problem
Source: 2010 Romania JBMO TST1 P2
Tags: angles, equal angles, geometry, convex quadrilateral