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In this diagram, the lines \( m \parallel n \) are parallel, and the transversal line intersects both parallel lines. You are asked to find the value of the angle \( x \).

Here is how to solve the problem:

### Step-by-step Explanation:

1. **Identify Corresponding Angles**: 
   Since the lines \( m \) and \( n \) are parallel, the angle marked \( x^\circ \) is a corresponding angle to the \( 113^\circ \) angle. Corresponding angles are equal when a transversal cuts two parallel lines.

2. **Conclusion**:
   Therefore, \( x^\circ = 113^\circ \).

Thus, the value of \( x \) is \( 113^\circ \).

Would you like a more detailed explanation, or do you have any other questions?

### Related Questions:
1. What are alternate interior angles, and how are they used in problems involving parallel lines?
2. How do you prove that corresponding angles are equal when two lines are parallel?
3. Can you explain the difference between supplementary and corresponding angles?
4. How can you use the sum of angles on a straight line to find missing angles?
5. In what other cases do transversal lines create equal angles?

**Tip**: Always look for angle relationships such as corresponding angles, alternate interior angles, or vertically opposite angles when working with parallel lines and transversals.

In this geometry problem, learn how to find the value of x when two parallel lines are cut by a transversal. The solution involves understanding corresponding angles, a key concept when dealing with parallel lines. Suitable for students in Grades 7-9.

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