2. In $\triangle A B C$, it is known that $\angle A B C=70^{\circ}$, $\angle B A C=80^{\circ}$, and $P$ is a point inside $\triangle A B C$ such that $\angle C B P$ $=\angle B C P=10^{\circ}$. Find $\angle B A P$.
Hint: It is easy to get $B P=C P$,
$$
\angle B A C=\frac{1}{2} \angle B P C \text {. }
$$

From criterion 2, we know that $P$ is the circumcenter of $\triangle A B C$.
Answer: $60^{\circ}$.