Example 2. In the equilateral $\triangle A B C$, $P$ is a point on side $B C$. Then, in the new triangle formed by $A P, B P, C P$ as sides, the largest interior angle is $\theta_{1}$, then ( ).
(A) $\theta \geqslant 90^{\circ}$
(B) $\theta \leqslant 120^{\circ}$
(C) $\theta=120^{\circ}$
(D) $\theta=135^{\circ}$
Solution: Obviously, $P$ on side $BC$ can be regarded as an extreme case or example of $P$ inside $\triangle ABC$.
Thus, from the conclusion of the previous problem, we know that the angles formed by the lines connecting $P$ with the three vertices of the triangle are $\alpha$,
$$
\beta, 180^{\circ} \text {, }
$$

Therefore, the largest interior angle of the triangle with sides $PA, PB, PC$ is $180^{\circ}-60^{\circ}=120^{\circ}$. Hence, the answer is C.