Given an isosceles $ABC$ triangle ($AB=AC$), and points $D,E$ on sides $AC, AB$, respectively, such that $AD<AE$. Suppose that angles $\angle BAC, \angle DBC, \angle ECB, \angle EDB$ are integers in degrees. Also let $\angle BAC=\angle EDB$.
What are the possible values $\angle BAC$ and $\angle DBC$? I’ve done some research and the possible $(\angle BAC, \angle DBC)$ pairs are $(12,42),(12,66),(20,70)$. My question is: how to find these with euclidean maths? Why these are the only possible values? If you just find some connection between these two angles, please post it, because it is really helpful.
Soon I post a figure I hope. Thanks in advance!
(This would be my lemma in a problem)