Question

in the diagram below, (overline{de}) is parallel to (overline{xy}). what is the value of (x)?

Explanation:

Step1: Identify angle - type relationship

Since $\overline{DE}$ is parallel to $\overline{XY}$, the 65 - degree angle and the angle adjacent to $x$ are corresponding angles. Corresponding angles are equal when two lines are parallel. So the angle adjacent to $x$ is 65 degrees.

Step2: Use linear - pair property

The angle adjacent to $x$ and $x$ form a linear pair. A linear pair of angles is supplementary, meaning their sum is 180 degrees. Let the adjacent angle be $a = 65^{\circ}$. Then $x + a=180^{\circ}$.

Step3: Solve for $x$

We substitute $a = 65^{\circ}$ into the equation $x + a = 180^{\circ}$. So $x=180 - 65=85^{\circ}$.

Answer:

C. 85