In the diagram, $A B$ is parallel to $D C$ and $A C E$ is a straight line. The value of $x$ is
(A) 35
(B) 30
(C) 40
(D) 45
(E) 50

![](https://cdn.mathpix.com/cropped/2024_04_20_6027bc27089ed4fc493cg-057.jpg?height=328&width=395&top_left_y=1099&top_left_x=1323)
Since $\angle A C E$ is a straight angle, $\angle A C B=180^{\circ}-105^{\circ}=75^{\circ}$.

In $\triangle A B C, \angle B A C=180^{\circ}-\angle A B C-\angle A C B=180^{\circ}-75^{\circ}-75^{\circ}=30^{\circ}$.

Since $A B$ is parallel to $D C, \angle A C D=\angle B A C=30^{\circ}$ (alternate angles). In $\triangle A D C, \angle D A C=180^{\circ}-\angle A D C-\angle A C D=180^{\circ}-115^{\circ}-30^{\circ}=35^{\circ}$. Thus, the value of $x$ is 35 .

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-269.jpg?height=304&width=352&top_left_y=168&top_left_x=1602)

ANSWER: (A)