Math Problem Statement

Given m ∥ n, find the value of x.

Solution

In the given image, you are asked to find the value of xx given that lines mnm \parallel n (lines mm and nn are parallel).

You are provided with two angles:

  1. (6x+30)(6x + 30)^\circ
  2. (8x10)(8x - 10)^\circ

These angles appear to be corresponding angles because they are on the same side of the transversal and between the two parallel lines. Since corresponding angles are congruent (equal) when lines are parallel, we can set the two expressions equal to each other:

6x+30=8x106x + 30 = 8x - 10

Now, let's solve for xx.

Steps:

  1. Subtract 6x6x from both sides: 30=2x1030 = 2x - 10

  2. Add 10 to both sides: 40=2x40 = 2x

  3. Divide both sides by 2: x=20x = 20

Thus, the value of xx is 2020.

Would you like further details or have any questions?

Here are 5 related questions for further practice:

  1. What are corresponding angles and how do they relate to parallel lines?
  2. Can you calculate the actual angle measures using x=20x = 20?
  3. How would the solution change if the lines mm and nn were not parallel?
  4. What is the relationship between alternate interior angles in parallel lines?
  5. How can you prove two lines are parallel using angle relationships?

Tip: Always check if lines are parallel in geometry problems to use angle congruence properties effectively!

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Math Problem Analysis

Mathematical Concepts

Parallel Lines
Corresponding Angles
Linear Equations

Formulas

6x + 30 = 8x - 10

Theorems

Corresponding Angles Theorem

Suitable Grade Level

Grade 8-10