Use Nodal Analysis to determine V₁ and V₂.

The original circuit is shown in black. The RED items were added.

Also note that V₁ = V_A and V₂ = V_B

I will sum the currents INTO the nodes.

Node A: (Eq. A)

Node B: (Eq. B)

Solving the two equations yields

V_A = V₁ = 25 V

and

V_B = V₂ = 90 V