Why don't we need to consider \$R_4\$ and \$R_5\$ when why calculate \$I_1\$?
The short answers is that the value of I_T already incorporates the values for all of the other resistors and the voltage source, so if you know that, you don't need to know anything but the resistor values in question: R1 &amp; R2.

Circuit Theory

The first thing to do in these situations is rearrange the circuit to something that makes more sense to you. This is the equivalent circuit:







simulate this circuit &ndash; Schematic created using CircuitLab

So you see that R1 || R2 is in series with R4 || R5 as well as R3. Things in series have the same current but split the voltage, and things in parallel have the same voltage but split the current. To further confuse you, they named the current going through R2 as I1, but I'll refer to currents and voltage by their associated component, so I_R2 is the current through R2, and I_R1||R2 is the total current through the parallel resistors R1 and R2.

Here's the known equations relating voltage, current, and resistance:


Substituting the appropriate values from equations 4, 5, and 6 you will come up with the following relationships:



Equivalent relationships can be made regarding R4 and R5.