A point is an example of a degenerate triangle.
In 2D, euclidean, flat space. Can the term "degenerate triangle" also describe a triangle with two right angles, an angle of 0° degrees, one side of a finite non-zero length, and two sides of infinite length?
The 0° angle would be positioned on a point discontinuity and so be in two places, both infinitely far from the other two vertexes.
That depends on your definition of triangle and degenerate triangle. If we say that a triangle (degenerate or not) is the convex envelope of three distinct points in the plane, then your region is not a degenerate triangle, but obviously the situation is different if we define a triangle as the intersection of three distinct half-planes.