What is the Relationship Between Angles and Dimensions?

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Bananaman3579
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Three Dimensional Angles?!?

ok, this is a stretch. I have an idea. If there are angles, measured in units of 1/360th of a circle. what happens when you add the third dimension factor. I thought it would be somehow measured in units of like the area of a sphere divided by 360^2 maybe. The problem with area is that it changes depending on the size of the sphere. Then somehow I'm picturing a cone and a triangle. This is most easily applied to a cube, if there are more sides the 2 dimensional figure made for the cone would change.

I would like to know if there is ay actualy study of what I;m trying to describe.
 
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*I would know if there is any actual study based on what I'm trying to explain.
 
thanks that was pretty much exactly what i pictured in my head