Math Problem Statement

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

Solution

The diagram shows three parallel lines lmnl \parallel m \parallel n, and a transversal line that intersects all three of these parallel lines. We are given the angle 124124^\circ at the intersection of the transversal with line ll, and the angle xx^\circ at the intersection of the transversal with line mm. Our goal is to find the value of xx.

Key Concepts:

  1. Corresponding Angles Postulate: When a transversal crosses parallel lines, the angles in corresponding positions are equal.
  2. Linear Pair: Two angles on a straight line add up to 180180^\circ.

Solution Steps:

  1. From the diagram, the angle 124124^\circ and the unknown angle xx^\circ appear to be corresponding angles because they are on the same side of the transversal and in the same relative position with respect to the parallel lines. By the Corresponding Angles Postulate, these angles must be equal.

Thus: x=124x = 124^\circ

So, the value of xx is 124\boxed{124^\circ}.

Would you like further details or clarification?

Related Questions:

  1. What are alternate interior angles, and how can they be identified in a diagram like this?
  2. How would the solution change if the given angle was 5656^\circ instead of 124124^\circ?
  3. Can you explain the difference between corresponding angles and alternate exterior angles?
  4. How does the concept of supplementary angles apply to parallel lines and transversals?
  5. How could you calculate unknown angles if only one angle in a parallel-line diagram is provided?

Tip:

When dealing with parallel lines and a transversal, look for pairs of corresponding angles, alternate interior angles, or alternate exterior angles to simplify your angle calculations.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Parallel Lines
Transversals
Corresponding Angles
Linear Pair

Formulas

x = corresponding angle to 124°
Sum of angles on a straight line = 180°

Theorems

Corresponding Angles Postulate
Linear Pair Postulate

Suitable Grade Level

Grades 8-10