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.

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and the unknown source of the answer is

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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?)



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