[BMCDA]

It's not defined.

[general_re]

Which should hardly be a surprise, given the nature of the triangle we are describing, don't you think? ;)

IOW, the law of cosines still holds true, even in such a case - it is a law, after all. So to define an angle as "two lines diverging from a common point" is too restrictive - defining it in such a manner implicitly assumes that there is a length involved, when the formal relationship between the sides and angles of a triangle requires no such thing.