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To solve this problem, we need to use the properties of parallel lines cut by a transversal.

### Given:
- Line \( \overline{BD} \) is parallel to line \( \overline{XY} \).
- The angle marked as 76° is an alternate interior angle to the angle marked \( x \).

### Reasoning:
When two parallel lines are cut by a transversal, alternate interior angles are equal. Therefore:

\[
x = 76^\circ
\]

### Conclusion:
The value of \( x \) is \( 76^\circ \).

### Answer:
The correct option is **A. 76**.

Would you like further details or have any questions?

Here are 5 related questions that expand on this topic:
1. What are corresponding angles in the context of parallel lines?
2. How do you determine if two angles are supplementary or complementary?
3. What are some other properties of angles formed by parallel lines and a transversal?
4. How can you prove lines are parallel if you only know certain angle measures?
5. What is the sum of all angles in a quadrilateral, and how does this relate to parallel lines?

**Tip:** Remember that alternate interior angles are always equal when two parallel lines are cut by a transversal!

In the diagram below, \(\overline{BD}\) is parallel to \(\overline{XY}\). What is the value of x?

This problem involves finding the value of x using the properties of parallel lines cut by a transversal. Learn how to apply the Alternate Interior Angles Theorem in a straightforward geometry problem suitable for students in Grades 6-8.

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