In the diagram, line segments $P Q$ and $R S$ intersect at $T$.

The value of $x$ is
(A) 30
(B) 20
(C) 40
(D) 50
(E) 35

![](https://cdn.mathpix.com/cropped/2024_04_20_6ed09463f225f8ba1f07g-050.jpg?height=398&width=612&top_left_y=2186&top_left_x=1125)
Since the sum of the angles in a triangle is $180^{\circ}$, then $\angle Q T R=180^{\circ}-\angle T Q R-\angle Q R T=180^{\circ}-50^{\circ}-90^{\circ}=40^{\circ}$. Since opposite angles are equal, then $\angle S T P=\angle Q T R=40^{\circ}$. Since the sum of the angles in $\triangle S T P$ is $180^{\circ}$, then

$$
\begin{aligned}
\angle P S T+\angle S P T+\angle S T P & =180^{\circ} \\
x^{\circ}+110^{\circ}+40^{\circ} & =180^{\circ} \\
x+150 & =180 \\
x & =30
\end{aligned}
$$

![](https://cdn.mathpix.com/cropped/2024_04_20_faa9db06d997f2a5b9b1g-087.jpg?height=398&width=615&top_left_y=202&top_left_x=1357)

Therefore, the value of $x$ is 30 .

ANSWER: (A)