The perpendicular lines are there in my 2D picture and they are perpendiculear to the bottom of the page for illustration purpose only.
The important line, is the line from the edge of the CB to the opposite edge of the OB for a 90 degree cut and can be sighted using the cue stick at the edge of the CB and aimed at the opposite edge on the OB while standing or down on the table over the cue. Also for starters, one can aim the cue from the edge of the CB to the same edge on the OB for a straght in shot, or one can aim the center of the CB at the center of the OB - that's easier and simpler.
Most of these sight lines are not perpendicular to anything else.
One can aim the edge of the CB at the center of the OB for a 30 degree cut, but it is easier to aim the center of the CB at the edge of the OB - that's easier.
It has been posted here that a particular good shooter aims the edge of the CB at the edge and I presume at perceptable fractions (to him) on the equator of the OB for thin cuts greater than 30 degrees rather than at the cloth or far rail as would be the case with center CB aiming at the GB - I often do.
The perceptable fractions on the OB are associated with all of the cut angles and are learned by practice and commited to memory. Since the CB and OB are round, there is no liniar relationship, for thick cuts the fractions are about the same, but get smaller as the cut gets thinner and rapidly gets smaller as the cut approaches 90 degrees.
Be well.
In my video of the 'Ultimate Aiming System" I show, demonstrate, and explain exactly how this system works....and aligns to all other systems in some way, shape or form ("aiming" systems help create angles).