Spherical Angle Math: Pyramid Angles Constant?

[ddddd28]

Hi,
Calculating the angles in 3D shapes can be a very frustrating and annoying thing. So, I was wondering, are there any mathematical terms, which describe a 3d angles?( "angles" between three lines- part of a sphere)
If there are such terms, suppose a triangular pyramid. Is the sum of those "angles" is a constant? just as the sum of angles in a triangle is 180 degrees.

 

[mfb]

Solid angle?
There are some formulas for the solid angles in a pyramid in that article.

 

[Khashishi]

The sum of the inner angles is not constant. However, the sum of the outer angles is constant. See https://www.maa.org/sites/default/files/pdf/upload_library/22/Ford/CarlBAllendoerfer.pdf