Question 59
Let $ABC$ be a triangle and $P$ a point inside it. Let $H$ be the point on side $BC$ such that the bisector of angle $\widehat{AHP}$ is perpendicular to line $BC$. Given that $\widehat{ABC}=\widehat{HPC}$ and $\widehat{BPC}=130^\circ$, determine the measure of angle $\widehat{BAC}$.