Real numbers are 1-dimensional in that they all fit in just one continuous line, so there are only 2 directions you can face in that line - forwards and backwards - hence only 2 possible values for rotation (quite literally it's a binary option).

So when mapping the rotation around on a plane (i.e. a 2D rotation) to a 1D rotation, because the 2D rotation is a range of possibilities you need to pick 2 and only 2 positions out of the infinite possibilities and they both must obbey they rule that you rotate in 2D from one to the other one you end up facing the opposite direction.

As it so happens any 2 numbers for a 2D angle of rotation that differ by 180 degrees or PI radians obbey both rules so any such pair of numbers can be used. Because in 2D rotations, there is the property that any rotation angle is equivalent to any angle which differs from it by a multiple of +/- 360° that gives you more rotation value pairs which have different numbers but represent the same rotation.

For simplicity, the tendency is to use 0° and 180°, but anything that obbeys the rules above would work, say -270 and +90, or 96 and 276 as long as you can form a straight line in the 2D plane for that rotation passing both angles and the center of rotation you can use them to express 1D rotations.