MathNet 2008-part-01 — 165 problems (EN–VI) Question 3

Let $ABC$ be a triangle with $\hat{B} = 40°$. It is known that there is a point $P$ on the bisector of angle $\hat{B}$ such that $BP = BC$ and $\hat{B}AP = 20°$. Determine the measures of the angles $\hat{A}$ and $\hat{C}$.