The more correct way to look at it is that pi is a numerical value that corresponds to 180 degrees. This is important because degrees don't exist on our numbering system and hence you cannot use the numerical values of degrees/minutes/seconds to work out critical lengths such as that of a circle or the area of a segment.
Basically, 1 pi (which is referred to as radian measure) is the result of dividing the circumference of a semi circle by its radius length (hence the term radian measure). This is why 1 pi rad is equated to 180 degrees (because there are 180 degrees from the first quadrant to the second in a semi circle)
And once you have this value pi (3.142 etc..), you use it as a standard for finding other values.
eg.
if 1 pi radians = 180 degrees
then 2 pi radians must be twice the size of 1 pi radians, which is 360 degrees.
so if you get something like n degrees which you want to convert into radian measure, you say: x = n/180*pi
Simple? I thought so.