What is the range of the sum of a sperical triangle's interior angles? Is it (π, 2π) or (π, 3π)? My high school textbook says it is (π, 2π), but some websites say it is (π, 3π).
In a small triangle on the face of the earth, the sum of the angles is only slightly more than 180 degrees. On a sphere, however, the corresponding sum is always greater than 180° but also less than 540°.
I found image
The diagram shows the spherical triangle with vertices A, B, and C. The angles at each vertex are denoted with Greek letters α, β, and γ. The arcs forming the sides of the triangle are labeled by the lower-case form of the letter labeling the opposite vertex.