In the diagram, $D A=C B$. What is the measure of $\angle D A C$ ?
(A) $70^{\circ}$
(B) $100^{\circ}$
(C) $95^{\circ}$
(D) $125^{\circ}$
(E) $110^{\circ}$

![](https://cdn.mathpix.com/cropped/2024_04_20_6ed09463f225f8ba1f07g-149.jpg?height=339&width=475&top_left_y=568&top_left_x=1302)
In the diagram, $D A=C B$. What is the measure of $\angle D A C$ ?
(A) $70^{\circ}$
(B) $100^{\circ}$
(C) $95^{\circ}$
(D) $125^{\circ}$
(E) $110^{\circ}$

![](https://cdn.mathpix.com/cropped/2024_04_20_faa9db06d997f2a5b9b1g-253.jpg?height=374&width=529&top_left_y=496&top_left_x=1362)

## Solution

$$
\text { In } \begin{aligned}
\triangle A B C, \angle B A C & =180^{\circ}-\left(70^{\circ}+55^{\circ}\right) \\
& =55^{\circ}
\end{aligned}
$$

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

We are given that $D A=C B$, so $D A=A C$ and $\triangle A D C$ is also isosceles.

Thus, $\angle A D C=\angle A C D=40^{\circ}$

and $\angle D A C=180^{\circ}-\left(40^{\circ}+40^{\circ}\right)$

$$
=100^{\circ}
$$

ANSWER: (B)