In the diagram, $P Q=P R$ and $\angle Q R P=65^{\circ}$. The value of $x$ is
(A) 45
(B) 30
(C) 50
(D) 60
(E) 40

![](https://cdn.mathpix.com/cropped/2024_04_20_e85ef69091c57cb633f3g-086.jpg?height=328&width=331&top_left_y=1858&top_left_x=1298)
Since the sum of the angles in any triangle is $180^{\circ}$, then looking at $\triangle Q S R$, we have

$$
\angle S Q R=180^{\circ}-\angle Q S R-\angle S R Q=180^{\circ}-90^{\circ}-65^{\circ}=25^{\circ}
$$

Since $P Q=P R$, then $\angle P Q R=\angle P R Q$.

Thus, $x^{\circ}+25^{\circ}=65^{\circ}$ or $x+25=65$, and so $x=40$.

ANswer: (E)