In the diagram, three lines meet at the points $A, B$ and $C$. If $\angle A B C=50^{\circ}$ and $\angle A C B=30^{\circ}$, the value of $x$ is
(A) 80
(D) 60
(B) 30
(C) 100
(E) 50

![](https://cdn.mathpix.com/cropped/2024_04_20_46ead6524a8d61e21c51g-085.jpg?height=341&width=287&top_left_y=266&top_left_x=1388)

Part B: Each correct answer is worth 6.
Since the sum of the angles in a triangle is $180^{\circ}$, then

$\angle B A C=180^{\circ}-30^{\circ}-50^{\circ}=100^{\circ}$.

Since a straight line makes an angle of $180^{\circ}$, then $x^{\circ}+100^{\circ}=180^{\circ}$ or $x=80$.

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-365.jpg?height=350&width=290&top_left_y=573&top_left_x=1424)

ANswer: (A)

## Part B