In the diagram, if $\angle P Q R=48^{\circ}$, what is the measure of $\angle P M N$ ?
(A) $60^{\circ}$
(B) $42^{\circ}$
(C) $48^{\circ}$
(D) $66^{\circ}$
(E) $84^{\circ}$

![](https://cdn.mathpix.com/cropped/2024_04_20_6ed09463f225f8ba1f07g-099.jpg?height=330&width=618&top_left_y=941&top_left_x=1100)
In $\triangle P Q R$, since $P R=R Q$, then $\angle R P Q=\angle P Q R=48^{\circ}$.

Since $\angle M P N$ and $\angle R P Q$ are opposite angles, then $\angle M P N=\angle R P Q=48^{\circ}$.

In $\triangle P M N, P M=P N$, so $\angle P M N=\angle P N M$.

Therefore, $\angle P M N=\frac{1}{2}\left(180^{\circ}-\angle M P N\right)=\frac{1}{2}\left(180^{\circ}-48^{\circ}\right)=\frac{1}{2}\left(132^{\circ}\right)=66^{\circ}$.

ANSWER: (D)