IMO 2018
PROBLEM 6
 
A convex quadrilateral $ABCD$ satisfies $AB\cdot CD$ = $BC\cdot DA$. Point $X$ lies inside $ABCD$ so that $\angle{XAB} = \angle{XCD}$ and $\angle{XBC} = \angle{XDA}$.
Prove that $\angle{BXA} + \angle{DXC} = 180$.