In the diagram, $T U$ is parallel to $P S$ and points $Q$ and $R$ lie on $P S$. Also, $\angle P Q T=x^{\circ}, \angle R Q T=(x-50)^{\circ}$, and $\angle T U R=(x+25)^{\circ}$.

![](https://cdn.mathpix.com/cropped/2024_04_20_e85ef69091c57cb633f3g-039.jpg?height=238&width=723&top_left_y=1152&top_left_x=663)

What is the measure of $\angle U R S$ ?
(A) $115^{\circ}$
(B) $140^{\circ}$
(C) $135^{\circ}$
(D) $130^{\circ}$
(E) $120^{\circ}$

## Part B: Each correct answer is worth 6.
Since $P Q R$ is a straight angle, then $\angle P Q T+\angle R Q T=180^{\circ}$.

Therefore, $x^{\circ}+(x-50)^{\circ}=180^{\circ}$ and so $2 x-50=180$ or $2 x=230$, which gives $x=115$.

Therefore, $\angle T U R=(x+25)^{\circ}=140^{\circ}$.

Since $T U$ and $P S$ are parallel, then $\angle U R S$ and $\angle T U R$ are alternating angles, which means that $\angle U R S=\angle T U R=140^{\circ}$.

ANSweR: (B)