Math Problem Statement

Given m ∥ n, find the value of x, where the angles are represented as (2x - 4)° and (3x - 12)°.

Solution

To solve this problem, we are given two parallel lines, mm and nn, and two angles formed by a transversal intersecting these lines. The expressions for the angles are (2x4)(2x - 4)^\circ and (3x12)(3x - 12)^\circ.

Since the lines mnm \parallel n, the angles are corresponding angles, which means they must be equal. Therefore, we can set the two angle expressions equal to each other and solve for xx:

2x4=3x122x - 4 = 3x - 12

Now, let's solve this equation step by step:

  1. Subtract 2x2x from both sides to isolate xx on one side: 4=x12-4 = x - 12

  2. Add 12 to both sides to solve for xx: 8=x8 = x

Thus, the value of xx is x=8x = 8.


Do you want more details on this solution, or do you have any questions?

Here are five related questions to deepen your understanding:

  1. What are alternate interior angles, and how do they relate to parallel lines?
  2. How would the solution change if the angles were vertical angles instead of corresponding angles?
  3. Can you think of a real-life example where parallel lines and transversals appear?
  4. What would happen if the two lines were not parallel? How would that affect the angle relationships?
  5. How can you verify that your solution for xx is correct?

Tip: Always check if the lines in the diagram are parallel before assuming angle relationships like corresponding angles or alternate interior angles.

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Math Problem Analysis

Mathematical Concepts

Geometry
Parallel Lines
Transversal
Algebra

Formulas

2x - 4 = 3x - 12

Theorems

Corresponding Angles Postulate

Suitable Grade Level

Grades 8-10