In the diagram the triangle shown is isosceles with $A B=A C$. The value of $x$ is
(A) 40
(B) 55
(C) 35
(D) 50
(E) 35

![](https://cdn.mathpix.com/cropped/2024_04_20_6ed09463f225f8ba1f07g-152.jpg?height=377&width=593&top_left_y=1579&top_left_x=1384)
Solution

Since $\triangle A B C$ is isosceles, $\angle A B C=\angle A C B$.

The value of each of these angles is $\frac{\left(180^{\circ}-40^{\circ}\right)}{2}=70^{\circ}$.

Since the points $B, C$, and $D$ lie on a straight line,

$$
\begin{aligned}
70+2 x & =180 \\
2 x & =110 \\
x & =55
\end{aligned}
$$

![](https://cdn.mathpix.com/cropped/2024_04_20_faa9db06d997f2a5b9b1g-262.jpg?height=349&width=458&top_left_y=365&top_left_x=1424)

ANSWER: (B)