Solving for current through a wire
Like the comment above suggested, if using mesh analysis, you need a third loop that has a voltage source from Vdd to ground.  Then you can solve for the three loop currents and subtract I2 from I1 to obtain the solution. The algebra is a bit messy.  A perhaps simpler approach is to convert the left and right sides to their Thevenin equivalents which reduces the problem to a single loop:







simulate this circuit &ndash; Schematic created using CircuitLab