# 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).

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