360 degrees = 2pi radians
180 degrees = pi radians
The unit circle has a radius of 1, based on the term "unit" meaning "one".
Since r = 1, this means the circumference is C = 2*pi*r = 2*pi*1 = 2pi
The distance around the unit circle is 2pi units, which corresponds to 2pi radians of a full revolution. Half of this is pi radians, which corresponds to 180 degrees.