VMO 1992 Problem 1

ABCD is a tetrahedron. The three face angles at A sum to $180^o$, and the three face angles at B sum to $180^o$. Two of the face angles at C, ∠ACD and ∠BCD, sum to $180^o$. Find the sum of the areas of the four faces in terms of AC + CB = k and ∠ACB = x.