In the diagram, $P R T$ and $Q R S$ are straight lines.

What is the value of $x$ ?
(A) 45
(B) 50
(C) 55
(D) 60
(E) 65

![](https://cdn.mathpix.com/cropped/2024_04_20_e85ef69091c57cb633f3g-092.jpg?height=434&width=352&top_left_y=1976&top_left_x=1296)
Since $P Q=Q R$, then $\angle Q P R=\angle Q R P$.

Since $\angle P Q R+\angle Q P R+\angle Q R P=180^{\circ}$, then $40^{\circ}+2(\angle Q R P)=180^{\circ}$, so $2(\angle Q R P)=140^{\circ}$ or $\angle Q R P=70^{\circ}$.

Since $\angle P R Q$ and $\angle S R T$ are opposite angles, then $\angle S R T=\angle P R Q=70^{\circ}$.

Since $R S=R T$, then $\angle R S T=\angle R T S=x^{\circ}$.

Since $\angle S R T+\angle R S T+\angle R T S=180^{\circ}$, then $70^{\circ}+2 x^{\circ}=180^{\circ}$ or $2 x=110$ or $x=55$.

ANSWER: (C)