help geometry

since in $\triangle ABC$, $\overset{-}{AB}=\overset{-}{AC}$, it means that it is an isosceles triangle, which also means that both angles at the bottom are going to be the same

 

so we know that $\angle ABC=\angle ACB=50^\circ$

 

by adding the two you get $50^\circ+50^\circ=100^\circ$

 

a triangle's interior angle are equal to $180^\circ$

 

knowing that $ \angle ABC+\angle ACB+ \angle BAC=180^\circ  $, by plugging in what we have we get $ 100^\circ+\angle BAC=180^\circ  $

 

$  \angle BAC=180^\circ-100^\circ   $

 

$ \boxed{ \angle BAC=80^\circ } $