# Where do the tributary angles/ratios for tributary areas come from?

When preparing load calculations for a slab, the quick method is to define the tributary areas of a slab for the beams/columns below. These are generally taken as lines at mid-span of the slab panels and, depending on the support conditions, at the edges at angles of 30 & 60 or 45 & 45 degrees.

Where do the 60/30 and 45/45 angle ratios come from? Example distributions are shown in the image below.

I know that in reality the ratios depend on the stiffness and end conditions of the various structural members, I also take it that the tributary areas are somewhat affected by the load they are carrying. Would excessive loading on one panel, compared to the adjacent panel affect the areas?

Also, different loads in different panels shouldn't affect the tributary areas due to the superposition principle. Assuming this principle is valid, the result of loading slab $A$ with $Q_A$ and slab $B$ with $Q_B$ should be equal to loading only slab $A$ and then adding the results due to loading only slab $B$.
This is obviously different from saying that loading slab $B$ won't affect slab $A$: any load applied to one slab will always generate stresses in neighboring, joined slabs (a fact usually ignored). It merely means that loading one slab won't affect the calculated tributary areas for another.