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This is sort of an extension of problem I had previously come across, where they had given us angles ABE and ADE as $20^{\circ}$ and $25^{\circ}$ respectively and asked us to find angle BEC, we had to notice that E fell on a circle with center C and radius BC, because angle BED is $135^{\circ}$, my question is, given that ABE is some angle $\theta_1$ and ADE is some other angle $\theta_2$, can we find every other angle in the figure.

Jeeth2006
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  • Yes. You can find the coordinates of point $E$ in terms of the given angle and the length of the side. From there you can find all angles. In fact, the length of the side is not important for angles. You can use a generic $L$ value, that will cancel in the calculations of all angles. – Andrei Feb 07 '22 at 16:46
  • Use the technique presented https://math.stackexchange.com/questions/4229579/find-the-angles-of-given-triangle-abc/4360511#4360511, you can calculate them by letting $\angle DAE$=x, using angular Ceva's theorem to represent $\tan x$ then solve it. – JetfiRex Feb 07 '22 at 23:28

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