One of Kirchhoff's Laws, namely Kirchhoff's Voltage Law, states that the voltage around any closed loop within a circuit is 0.
Work Step by Step
In order to apply Kirchhoff's Voltage Law correctly, one must define the current in every loop in the circuit. (This is necessary for the resistors, but it is not necessary for the batteries. After all, when the current is defined, it is necessary to use the equation $V=IR$. When going in the direction of the current, this value is positive, but when going against the current, this value is deemed to be negative.) Next, one must be sure to pay attention to the defined higher and lower potential of each of the batteries, where the side of higher potential is denoted by a positive and where the side of lower potential is denoted using a negative sign. Finally, one can traverse the loop, adding the voltage for each battery/resistor that is gone through when the path is considered. Note, when going through a battery, the voltage is deemed to a positive change when going from lower to higher potential, and it is deemed to be negative when going from higher to lower potential. Once the whole path is considered, the sum of the positive and negative voltages should be set equal to zero, adhering to Kirchhoff's Voltage Law.