Question

lines a, b, c, and d intersect as shown. what is y? a. 42 b. 85 c. 88 d. 95

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. The angle vertical to the one marked $42^{\circ}$ is also $42^{\circ}$.

Step2: Use angle - sum property of a triangle

The sum of angles in a triangle is $180^{\circ}$. In the triangle where one angle is $42^{\circ}$ and another is $50^{\circ}$ (since $180-(95 + 35)=50^{\circ}$, and we know that the vertical - angle of the $42^{\circ}$ angle is in this triangle). Let the third angle be $y$. Then $y+42 + 50=180$.
We can calculate $y$ as follows:
\[y=180-(42 + 50)=88^{\circ}\]

Answer:

C. 88