Finding relevant voltages and current in a BJT
There would be at least three loops since Vcc is really an ideal voltage source connected to ground. But mesh analysis is not a good way to solve this problem.

You need to understand the relationship between Ib, Ic, and Ie, which is based on the transistor's beta (hFE). This circuit is a standard common emitter amplifier topology. If this is homework, you probably should have covered CE amplifiers in class by now. If you haven't, that's unfortunate. :-)

The first step is to know that the equivalent input resistance looking into the base is equal to beta * Re. This lets you calculate the base voltage. From there, assume the transistor is in active mode and calculate the other voltages and currents one at a time.