how to find the angle between two angle without coordinate system

If there are vectors V, A, B, and C starting from a common point O but no coordinate system is given.

I know to find the angle between two vector, we could use a dot product between the vectors. For example, the angle between vector V and A will be $$\arccos(V\cdot A)/(|V|*|A|)$$, similar idea to find the angle between vector V and B, vector V and C.

Since the order of vector in the dot product does not matter, so the angle between V,B and the anvle between V, C are same. My question is, if I used vector v as a reference always, and I would like the angle defined counter-clockwise such that the angle between V, B is 160 degree and the angle between V, C is 200 degee. Anyway to find the angle between two vector defined in that way? Thanks.