Question 154
In a triangle $ABC$, let segment $AP$ bisect $\angle BAC$, with $P$ on side $BC$, and let segment $BQ$ bisect $\angle ABC$, with $Q$ on side $CA$. It is known that $\angle BAC = 60^\circ$ and that $AB + BP = AQ + QB$. What are the possible angles of triangle $ABC$?