I am trying to understand the angle and side measurements of triangles that are degenerate. There are 3 types of these triangles: https://en.wikipedia.org/wiki/Degeneracy_(mathematics)#Triangle
For the one whose 2 vertices are equal, they state that two of the angles are undefined and the third one is 0 degrees. Well, I wonder how this thing qualifies for a triangle if the sum of the angles must be 180 degrees by definition (undefined + undefined + 0 is not 180). I also can't figure out which of the 3 vertices have undefined angles and which one has 0 angle.
It also doesn't say what angle measurements has the triangle whose vertices are all equal. (I wonder.)
Please help me out with these, and thank you.
By the way, while searching for answers yesterday, I stumbled on a resource that says that the angles of the 2nd example (on the image above) should be 90, 90, 0. Which confused me more. Take a look (notice alpha, beta, and gamma angle measurements; they are given as 90, 90, 0): 