Questions: In the diagram below, BD→ is parallel to XY→. What is the value of x? A. 125 B. 75 C. 55 D. 115

Transcript text: 1.8.3 Quiz: Parallel Lines and Proofs In the diagram below, $\overrightarrow{B D}$ is parallel to $\overrightarrow{X Y}$. What is the value of $x$ ? A. 125 B. 75 C. 55 D. 115

Solution

Solution Steps

Step 1: Identify the given information

We are given that line $ \overline{BD} $ is parallel to line $ \overline{XY} $ and that the angle between the transversal and $ \overline{BD} $ is 125°.

Step 2: Recognize the relationship between angles

Since $ \overline{BD} $ is parallel to $ \overline{XY} $, the angles formed by the transversal are either corresponding angles or alternate interior angles. The angle given (125°) and the angle $ x $ are alternate interior angles.

Step 3: Apply the properties of parallel lines

Alternate interior angles are equal when the lines are parallel. Therefore, the measure of angle $ x $ is equal to the measure of the given angle, which is 125°.