https://file.aiquickdraw.com/mathbot/file/1731030005716skbfl89q.jpg

To solve for \( x \) in this problem, let's analyze the diagram given that lines \( l \), \( m \), and \( n \) are parallel.

### Solution Steps

1. **Identify Angle Relationships:**
   Since \( l \parallel m \parallel n \), we know that the angles formed by a transversal with parallel lines have specific relationships, particularly corresponding and alternate interior angles.

2. **Angle Correspondence:**
   The angle marked as \( 135^\circ \) forms an alternate interior angle with the angle marked as \( x^\circ \). Therefore, \( x \) and \( 135^\circ \) are equal because they are alternate interior angles.

3. **Conclusion:**
   \[
   x = 135^\circ
   \]

Thus, the value of \( x \) is \( 135^\circ \).

Would you like a further breakdown of these steps or have any questions?

Here are some related questions you might find useful:
1. How do alternate interior angles work when dealing with parallel lines?
2. What are corresponding angles, and how are they used in parallel line problems?
3. How can we use angle relationships to solve for unknown angles without knowing all angles in the diagram?
4. What role does the transversal play in determining angle relationships in parallel line problems?
5. How can we verify that angles are equal in diagrams with parallel lines?

**Tip:** When solving problems involving parallel lines and transversals, look for alternate interior and corresponding angle pairs, as they often simplify the solution process.

Given l ∥ m ∥ n, find the value of x.

Learn how to determine the value of x when three parallel lines intersect a transversal line, with a given angle of 135°. This solution covers key concepts like parallel lines, transversal lines, and the Alternate Interior Angles Theorem. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation