In the diagram, $P Q R$ is a straight line.

The value of $x$ is
(A) 72
(B) 44
(C) 58
(D) 64
(E) 52

![](https://cdn.mathpix.com/cropped/2024_04_20_6ed09463f225f8ba1f07g-092.jpg?height=273&width=434&top_left_y=1479&top_left_x=1214)
Solution 1

Since $\angle P Q S$ is an exterior angle of $\triangle Q R S$, then $\angle P Q S=\angle Q R S+\angle Q S R$, so $136^{\circ}=x^{\circ}+64^{\circ}$ or $x=136-64=72$.

## Solution 2

Since $\angle P Q S=136^{\circ}$, then $\angle R Q S=180^{\circ}-\angle P Q S=180^{\circ}-136^{\circ}=44^{\circ}$.

Since the sum of the angles in $\triangle Q R S$ is $180^{\circ}$, then $44^{\circ}+64^{\circ}+x^{\circ}=180^{\circ}$ or $x=180-44-64=72$.

ANSWER: (A)