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

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
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Solution

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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°.

Final Answer

The value of \( x \) is 125°.

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