# The Internal Angle Bisector

**Geometry**Level 3

In \(\triangle ABC\), \(\angle ABC = 30°.\) Points \(P\) and \(Q\) are chosen on \(\overline{AC}\) such that \(AP+BC= AB+CQ\). The internal angle bisector of \(\angle ABC\) intersects \(\overline{AC}\) at \(R\). Given that \(R\) is the midpoint of \(PQ\), find \(\angle BAC \) (in degrees).