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To solve the problem of finding the value of \( x \) for which lines \( l \) and \( m \) are parallel, we need to consider the properties of angles formed by parallel lines and a transversal.

### Steps to Solve:

1. **Identify the Angle Relationships:**
   - The problem involves alternate interior angles, as well as corresponding angles because when two lines are parallel, the alternate interior angles are equal, and corresponding angles are equal.
   - In the diagram, the 28° angle and the \( x \) angle are on the same side of the transversal, forming a linear pair with the angle adjacent to the 56° angle.

2. **Apply the Angle Sum Property:**
   - The sum of angles on a straight line is 180°. Therefore, the angle adjacent to the 56° angle is \( 180^\circ - 56^\circ = 124^\circ \).
   - Since \( x \) and 28° are corresponding angles when \( l \) is parallel to \( m \), we have \( x = 124^\circ - 28^\circ = 96^\circ \).

However, this approach might not align with the diagram. Let's instead rely on the rule that the alternate interior angles or corresponding angles must be equal for lines to be parallel.

3. **Alternate Interior Angles or Corresponding Angles:**
   - If \( l \) is parallel to \( m \), \( x \) must equal \( 56^\circ \) because they are corresponding angles.
   - Therefore, \( x = 56^\circ \).

### Conclusion:
The value of \( x \) that makes lines \( l \) and \( m \) parallel is \( 56^\circ \).

Would you like more details or have any questions about this? Here are five related questions to consider:

1. What are corresponding angles and how do they relate to parallel lines?
2. How can you use alternate interior angles to determine if two lines are parallel?
3. What is the angle sum property, and how is it applied in geometric problems?
4. Why do corresponding angles have to be equal for lines to be parallel?
5. How would the value of \( x \) change if the given angles were different?

**Tip:** When solving problems involving parallel lines and transversals, always look for angle pairs like corresponding angles, alternate interior angles, or co-interior angles to determine relationships between them.

Find the value of x for which line l is parallel to line m. The diagram includes a 28° angle and a 56° angle, with x being the unknown angle.

Learn how to find the value of x that makes lines l and m parallel using geometric principles. This problem focuses on understanding corresponding angles and the sum of angles on a straight line. Suitable for students in Grades 7-9.

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