Math Problem Statement

Given l || m || n, find the value of x.

Solution

In the image, the lines ll, mm, and nn are parallel, as indicated by the notation lmnl \parallel m \parallel n. There is a transversal intersecting these lines, forming angles, including the given angle of 137137^\circ and the unknown angle xx^\circ.

Using the fact that lmnl \parallel m \parallel n, we can apply the properties of alternate interior angles and supplementary angles formed by a transversal cutting through parallel lines.

Solution:

  1. The angle 137137^\circ and angle xx^\circ are supplementary angles, as they are on the same side of the transversal. Supplementary angles add up to 180180^\circ.

Thus, we can write the equation: x+137=180x + 137^\circ = 180^\circ

  1. Solving for xx: x=180137=43x = 180^\circ - 137^\circ = 43^\circ

Thus, the value of xx is 4343^\circ.

Would you like more 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 do corresponding angles behave when a transversal intersects parallel lines?
  3. What is the significance of supplementary angles in geometry?
  4. Can you explain the concept of vertically opposite angles?
  5. How do parallel line properties apply in real-world structures or designs?

Tip: When working with parallel lines and transversals, it's useful to remember the various angle relationships like alternate interior, corresponding, and supplementary angles.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Parallel Lines
Transversal
Supplementary Angles

Formulas

x + 137° = 180°

Theorems

Supplementary Angles Theorem

Suitable Grade Level

Grades 7-10