Line segments $P Q$ and $R S$ intersect at $T$, as shown. If $T S=T Q$ and $\angle P T R=88^{\circ}$, the value of $x$ is
(A) 44
(B) 46
(C) 88
(D) 45
(E) 50

![](https://cdn.mathpix.com/cropped/2024_04_20_6027bc27089ed4fc493cg-027.jpg?height=263&width=341&top_left_y=2319&top_left_x=1293)

Part B: Each correct answer is worth 6.
Line segments $P Q$ and $R S$ intersect at $T$ and so $\angle P T R$ and $\angle S T Q$ are opposite angles and therefore $\angle S T Q=\angle P T R=88^{\circ}$.

Since $T S=T Q$, then $\triangle S T Q$ is an isosceles triangle and so $\angle T S Q=\angle T Q S=x^{\circ}$.

The three interior angles of any triangle add to $180^{\circ}$.

Thus, $88^{\circ}+x^{\circ}+x^{\circ}=180^{\circ}$, and so $2 x=180-88$ or $2 x=92$ which gives $x=46$.

ANSWER: (B)