I,ve attached a word document with a problem I'm trying to help my nephew with in college. Any help would be greatly appreciated as it has been a while since I have done this.
The tension in the two cables is equal to mg, where m the the mass suspended from the cable.
Now resolve the forces in the cables at the middle pulley into vertical and horizontal components. The horizontal components are equal but opposite which will allow you to solve for the angle. The vertical components will sum to minus the gravitational force on the centre mass from which you finf the mass of D.