Answer by periblepsis for How to calculate the value of resistor R2?

Here's how I'd process the problem, in order:

1. There's no ground shown. Pick a node that looks good to me and call it \$0\:\text{V}\$ (or ground, so to speak.) In this case:

2. Assign known node voltages (known with respect to the ground reference just assigned):

3. Now, at this point I can see that I know the voltage difference across \$R_1\$ is \$15\:\text{V}-5\:\text{V}=10\:\text{V}\$ and also know the current through it is \$10\:\text{mA}\$. So I can work out its resistance using Ohm's Law. The same is also true now for \$R_2\$ and \$R_3\$, both of which will have \$5\:\text{V}-0\:\text{V}=5\:\text{V}\$ across them. (But you already knew that, of course.)

4. The only missing item is the current through \$R_2\$. But you already worked this out as \$10\:\text{mA}-2\:\text{mA}=8\:\text{mA}\$ (KCL.)

So everything needed to work out all three resistor values is known. Just apply Ohm's Law at this point and work out the values.

(Those are the mental steps I'd likely take, anyway, if left to my own devices and not where a teacher/assignment requires some other methods to be applied.)