In the diagram, triangle $A B C$ is isosceles, with $A B=A C$. If $\angle A B C=50^{\circ}$ and $\angle D A C=60^{\circ}$, the value of $x$ is
(A) 70
(B) 50
(C) 80
(D) 60
(E) 30

![](https://cdn.mathpix.com/cropped/2024_04_20_6027bc27089ed4fc493cg-083.jpg?height=301&width=412&top_left_y=1129&top_left_x=1323)
Since triangle $A B C$ is isosceles, $\angle A C B=\angle A B C=50^{\circ}$.

Since the sum of the angles in triangle $A C D$ is $180^{\circ}$, then

$$
\begin{aligned}
x^{\circ}+60^{\circ}+50^{\circ} & =180^{\circ} \\
x & =70
\end{aligned}
$$

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-372.jpg?height=312&width=436&top_left_y=1169&top_left_x=1343)

ANSwer: (A)