Question 164
Let $ABC$ be a triangle with centroid $G$. Points $R$ and $S$ are chosen on rays $GB$ and $GC$, respectively, such that
$$
\angle ABS = \angle ACR = 180^\circ - \angle BGC.
$$
Prove that $\angle RAS + \angle BAC = \angle BGC$.
$$
\angle ABS = \angle ACR = 180^\circ - \angle BGC.
$$
Prove that $\angle RAS + \angle BAC = \angle BGC$.