I was asked to find current I1 and I2 in the problem below using nodal analysis.

I found out the current to be V=13.33V, I1=3.33A and I2=0.7278A. I was later asked to find the same currents (I1 and I2) after the addition of a new resistor using mesh analysis.

After applying mesh analysis(supermesh),I got the same value for the two currents. How is it possible that the 2 currents were not altered by the new resistor? Also, How do i make sure the values I got are correct?