Hyperbolic Geometry: Defect of a triangle

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I'm working on a problem and I needed an angle I couldn't find, so I looked it up in the solution manual off chegg-com. And I do not understand what they are saying, can you help? I copied the entire solution into this pdf file.

I was following along just fine until the end of step 5.. what do they mean by "this is one of the defects"? As I understand it the defect of a triangle is a single number and there can't be two. (180 minus all three angles) Then at the end of step 7, they say here's another defect.

Can anyone explain this to me?

I'd ask my professor, but she's gone out of town (again) and won't be back until after this is due.