A question about spherical geometry

[qfxz]

What is the range of the sum of a spherical 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).

To be more clearly:

This is a spherical triangle ABC. What is the range of ∠CAB+∠ABC+∠BCA? Is it (π, 2π) or (π, 3π)?

 

[Dr.Peterson]

What is the range of the sum of a spherical 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).

To be more clearly:
View attachment 33482
This is a spherical triangle ABC. What is the range of ∠CAB+∠ABC+∠BCA? Is it (π, 2π) or (π, 3π)?

Did you find any websites that agree with your book? Those that I find all agree with this.

One quick check you can do is to imagine the largest possible spherical triangle, and what its angles would be. That will have a sum more than [imath]2\pi[/imath]!

I'm wondering if you might be misinterpreting what the book says. I'd like to see an image of what it says!