In the diagram, $\triangle P Q R$ and $\triangle S T U$ overlap so that $R T Q U$ forms a straight line segment. What is the value of $x$ ?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50

![](https://cdn.mathpix.com/cropped/2024_04_20_e85ef69091c57cb633f3g-069.jpg?height=314&width=660&top_left_y=1995&top_left_x=1098)
We label the point of intersection of $R P$ and $S U$ as $W$.

![](https://cdn.mathpix.com/cropped/2024_04_20_688a3b42f69739f2e244g-133.jpg?height=304&width=653&top_left_y=1889&top_left_x=796)

Now $\angle S W R$ is an exterior angle for $\triangle R W U$.

Therefore, $\angle S W R=\angle W R U+\angle W U R$, and so $50^{\circ}=30^{\circ}+x^{\circ}$ or $x=50-30=20$.

Alternatively, we could see that $\angle R W U=180^{\circ}-\angle S W R=180^{\circ}-50^{\circ}=130^{\circ}$.

Since the angles in $\triangle R W U$ add to $180^{\circ}$, then $30^{\circ}+130^{\circ}+x^{\circ}=180^{\circ}$, or $x=180-130-30=20$.

ANSWER: (B)