Math Problem Statement

Given l ∥ m ∥ n, find the value of x.

Solution

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

Problem Analysis:

  1. The lines ll, mm, and nn are parallel, and a transversal cuts across these lines.
  2. The angle marked as 6363^\circ is formed by the transversal and line ll.
  3. We need to find the value of xx^\circ, the angle formed by the transversal and line nn.

Solution:

Since lmnl \parallel m \parallel n, the transversal creates alternate interior angles, corresponding angles, and co-interior angles.

  1. The angle marked 6363^\circ is a corresponding angle with the angle on the same side of the transversal near line mm. Therefore, the angle formed by the transversal and line mm on the upper side is also 6363^\circ.

  2. The angle xx^\circ is on the opposite side of the transversal near line nn. Since xx^\circ and the previously found 6363^\circ angle are alternate interior angles, they are congruent.

Thus, x=63.x = 63^\circ.

Final Answer:

x=63.x = 63^\circ.

Would you like further details or have any questions?

Here are some related questions you might consider:

  1. What are alternate interior angles, and how do they relate to parallel lines?
  2. How can we determine corresponding angles in parallel lines cut by a transversal?
  3. What other types of angle relationships exist in parallel line configurations?
  4. How do co-interior angles help in solving for unknown angles?
  5. How do the properties of transversals help in real-life applications?

Tip: Always look for corresponding and alternate interior angles when dealing with parallel lines cut by a transversal.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Parallel Lines
Transversal
Corresponding Angles
Alternate Interior Angles

Formulas

-

Theorems

Alternate Interior Angle Theorem
Corresponding Angle Postulate

Suitable Grade Level

Grades 7-9