In the diagram, $A B$ is parallel to $C D$. What is the value of $y$ ?
(A) 75
(B) 40
(C) 35
(D) 55
(E) 50

![](https://cdn.mathpix.com/cropped/2024_04_20_e85ef69091c57cb633f3g-148.jpg?height=260&width=525&top_left_y=1884&top_left_x=1277)
In the diagram, $A B$ is parallel to $C D$. What is the value of $y$ ?
(A) 75
(B) 40
(C) 35
(D) 55
(E) 50

![](https://cdn.mathpix.com/cropped/2024_04_20_688a3b42f69739f2e244g-278.jpg?height=298&width=583&top_left_y=1580&top_left_x=1302)

## Solution

Since $A B$ is paralled to $C D$, then $\angle B M N+\angle M N D=180$.

Thus, $2 x+70=180$

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

Using $\triangle M N P, y=180-(70+55)$

$$
=55
$$

![](https://cdn.mathpix.com/cropped/2024_04_20_688a3b42f69739f2e244g-278.jpg?height=318&width=574&top_left_y=1966&top_left_x=1361)

ANSWER: (D)