In the diagram, line $L_{1}$ is parallel to line $L_{2}$ and $B A=B C$. The value of $x$ is
(A) 35
(D) 45
(B) 30
(C) 37.5
(E) 40

![](https://cdn.mathpix.com/cropped/2024_04_20_e85ef69091c57cb633f3g-123.jpg?height=290&width=504&top_left_y=1682&top_left_x=1212)
We label two more points on the diagram, as shown.

Then $\angle D E C=x^{\circ}$, since it is equal to its opposite angle.

Since line $L_{1}$ is parallel to line $L_{2}$, then $\angle D B C=70^{\circ}$, since $D B$ is a transversal, and $\angle B C A=x^{\circ}$ since $E C$ is a transversal.

Since $\angle D B C=70^{\circ}$, then $\angle A B C=110^{\circ}$, since these angles are supplementary.

Since $\triangle A B C$ is isosceles, then $\angle B A C=\angle B C A=x^{\circ}$, and so looking at the sum of the angles in $\triangle A B C$, we get

$$
\begin{aligned}
x^{\circ}+110^{\circ}+x^{\circ} & =180^{\circ} \\
2 x & =70 \\
x & =35
\end{aligned}
$$

![](https://cdn.mathpix.com/cropped/2024_04_20_688a3b42f69739f2e244g-224.jpg?height=347&width=614&top_left_y=802&top_left_x=1360)

ANSWER: (A)