PL-OM 1977 Problem 1

Let $ABCD$ be a tetrahedron with $\angle BAD = 60^{\cdot}$ , $\angle BAC = 40^{\cdot}$ , $\angle ABD = 80^{\cdot}$ , $\angle ABC = 70^{\cdot}$ . Prove that the lines $AB$ and $CD$ are perpendicular.