Am I correct to assume that the four inside angles of the main triangle should sum to 360 degrees? Mathematically this is tru for a four-side polygon but I'm wondering if frame builders deviate (by say 1 degrees) for some reason I'm not aware of.
The sum of the interior angels of a quadrangle is always 360º, there is no way around it.
180 (n-2) where n is the number of sides of the polygon.
You could put a bend in one of the pipes to make up for it, but I have not worked with metal and don't know if there is a reason one would want to do such.
Are you talking about adding up the lug angles from the ht/st/bb? Most lug angles are measured in relation to an imaginary vertical plane and can vary according to the design ie: road bike, track bike, amount of bb drop, sloping top tubes.....there is no reason the angles should add up to 360.