TITLE: Is it possible to find $\angle BOA$?
QUESTION [2 upvotes]: In triangle $ABC$ , $\angle BAC=80^o$ . suppose $O$ is a point in triangle $ABC$ that $OBC=30^\circ$ and $OCB=10^\circ$ . Is it possible to find $\angle BOA$ ?

REPLY [3 votes]: No, because take such a triangle $ABC$ with $O$ fixed and consider the circumcircle of $ABC$. Then you can move the point $A$ along the circle without changing $\angle OBC$,$\angle OCB$ and $\angle BAC$, but surely $\angle BOA$ will change.
{"set_name": "stack_exchange", "score": 2, "question_id": 1594140}