Math Problem Statement

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

Solution

This image represents two parallel lines mm and nn, intersected by a transversal. The angles at the intersection are given as:

  • (5x2)(5x - 2)^\circ on line mm
  • (x2)(x - 2)^\circ on line nn

The question asks to find the value of xx.

Since the lines mm and nn are parallel, the angles formed by the transversal crossing the two parallel lines are corresponding angles. Therefore, we can set the two angle expressions equal to each other:

5x2=x25x - 2 = x - 2

Now, let's solve for xx:

5xx=2+25x - x = -2 + 2 4x=04x = 0 x=0x = 0

So, the value of xx is 00.

Would you like me to go into further detail, or do you have any questions?

Here are some related questions:

  1. How do we solve for variables in angle equations like this one?
  2. What are corresponding angles, and how do they relate to parallel lines?
  3. What other types of angle relationships exist with parallel lines and transversals?
  4. How can we apply this principle in geometry proofs?
  5. How do you handle equations with multiple terms involving the variable?

Tip: When dealing with parallel lines cut by a transversal, always look for corresponding, alternate interior, or alternate exterior angles to set up equations.

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Math Problem Analysis

Mathematical Concepts

Parallel Lines
Transversal
Corresponding Angles
Algebraic Equations

Formulas

Corresponding Angles Theorem: If two parallel lines are cut by a transversal, then each pair of corresponding angles are equal.

Theorems

Corresponding Angles Theorem

Suitable Grade Level

Grades 8-10