For the n-town problem when n is 3 and the nodes may not necessarily form an equalateral triangle, I'm trying to prove that the angle between 2 adjacent roads is always 2pi/3 in the locally minimum solution (with one internal node).
I have proved that the sum of the unit vectors in the direction of the 3 roads (represented as vectors) is the zero vector. I have tried to manipulate the equality using the dot product but can't seem to prove it.