How to build a protractor without a protractor? We all know how to use a protractor, it is taught in elementary school. However, I was wondering what type of knowledge is required to build one from scratch. 
For instance, was the understanding of $\pi$ and a compass first required before the first protractor, and if so how can I draw a full protractor on paper with just a compass, a ruler and some understanding of $\pi$?
I guess my point is, if we can draw a semi-circle on paper, then how can we fill up the degrees without the help of a protractor?

I think there are two questions here: the practical question of what is actually done at a protractor factory, and the theoretical question of can you decompose a circle into $360$ equal pieces given only a straight-edge and compass.
I'll focus on the latter since the former is not really about mathematics. We know that $360 = 2^3\cdot3^2\cdot5$. Now, $72=2^3\cdot3^2$ degrees is a constructible angle, because a pentagon is constructive. Bisection is always possible, so that leaves angles that need to be trisected twice. This isn't possible with a straight-edge and compass (in general), BUT arbitrary trisection is possible with a ruler and compass (i.e. putting distances on your straight-edge is enough to over-come this hurdle). Wikipedia says this was already known to Archimedes.
