Is it possible to find $\angle BOA$? 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 $\angle BOA$ ?

No, because this only fixes the $OBC$ triangle upto congruency.

In other words, for any $ABC$ with $BAC=80$ (and variable $ABC$ and $ACB$), you can find the point $O$.

Here's what I mean -

**Triangle 1** ![enter image description here](

**Triangle 2**

![enter image description here](