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

If $x+y=76$, what is the value of $x$ ?
(A) 28
(B) 30
(C) 35
(D) 36
(E) 38

![](https://cdn.mathpix.com/cropped/2024_04_20_e85ef69091c57cb633f3g-015.jpg?height=364&width=687&top_left_y=1588&top_left_x=1074)
Since $P Q R$ forms a straight angle, then

$$
x^{\circ}+y^{\circ}+x^{\circ}+y^{\circ}+x^{\circ}=180^{\circ}
$$

which gives $3 x+2 y=180$.

Since $x+y=76$ and $2 x+2 y+x=180$, then $2(76)+x=180$ or $x=180-152=28$.

ANSWER: (A)

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