In the diagram, what is the value of $x$ ?
(A) 110
(B) 50
(C) 10
(D) 60
(E) 70

![](https://cdn.mathpix.com/cropped/2024_04_20_46ead6524a8d61e21c51g-068.jpg?height=315&width=339&top_left_y=1740&top_left_x=1294)
Since the angles in a triangle add to $180^{\circ}$, then the missing angle in the triangle is $180^{\circ}-50^{\circ}-60^{\circ}=70^{\circ}$.

We then have:

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-302.jpg?height=387&width=412&top_left_y=324&top_left_x=911)

Since $\angle B X C=70^{\circ}$, then $\angle A X C=180^{\circ}-\angle B X C=110^{\circ}$.

Since $\angle A X C=110^{\circ}$, then $\angle D X A=180^{\circ}-\angle A X C=70^{\circ}$.

Therefore, $x=70$.

(Alternatively, we could note that when two lines intersect, the vertically opposite angles are equal so $\angle D X A=\angle B X C=70^{\circ}$.)

ANSWER: (E)