The point of this exercise is to show you how labeling voltages at the beginning of a circuit analysis is an arbitrary choice. I analyze the same circuit two times and show the answer comes out right even if the orange voltage labels are different.
The second analysis starts at 4:50. Notice how the orange label for v_1 is “upside down” compared to the circuit on the left. Even with the label in this orientation the answer comes out the same as the first analysis.
Labeling voltages is not a matter of “right” and “wrong”. You are not trying to guess what the final answer will be. Voltage labels simply sets a reference direction for voltage.
Created by Willy McAllister.