Question 1
Let $ABCD$ be a tetrahedron such that the sums of the three face angles at $A$ and at $B$ are both $180^\circ$. The two face angles $\angle ACD$ and $\angle BCD$ at $C$ have sum $180^\circ$. Determine the sum of the areas of its four faces in terms of $k=AC+CB$ and $\angle ACB=x$.