In my previous question: Common rules in calculating angles of diagonal lines in quadrangle, using synthetic(axiomatic) geometry.
I wanted to know the common rule for calculating angles of diagonal lines in quadrangle only with axiomatic geometry, but I realized that only in special circumstances the angle can be calculated without involving the law of sines/cosines and trig functions.
The original question was.
and the unknown source of the answer is
My first question was in the original question, but it turned out there is no common rule.
The second question is, is there any other solution for this problem? I know that answers for axiomatic geometry problems can be ridiculous, but this is beyond imagination. (Or is this a well-known trick?)
