I came across this when I was trying to prove some properties of a particular parallelogram. It looked pretty trivial at first, but it looks like I've sneezed up the wrong tree with this one.
2026-05-13 17:27:02.1778693222
Looking for an elementary solution to this angle problem
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Applying the law of sines in the two smaller triangles and eliminating the lengths, you can show that
$$ \frac{\sin(a+b+x)}{\sin x} = \frac{\sin a}{\sin b} $$
From this you get
$$\sin(a+b) \cot x = \frac{\sin a}{\sin b} - \cos(a+b) $$
so you can solve for $\cot x$ and then for $x$. Is this what you need?