Math Problem Statement

Follow the steps below to find the value of x that makes lines A and B parallel. Set the alternate exterior angles equal to each other: 10x and 8x + 30.

Solution

From the image, we are solving for xx to make the two lines AA and BB parallel. The problem asks to use the fact that alternate exterior angles are equal when the lines are parallel.

Given:

The two alternate exterior angles are:

  • 10x10x
  • 8x+308x + 30

Step to solve:

Set the two angles equal to each other: 10x=8x+3010x = 8x + 30

Solve for xx:

  1. Subtract 8x8x from both sides: 10x8x=3010x - 8x = 30 2x=302x = 30

  2. Divide both sides by 2: x=15x = 15

Final Answer:

x=15x = 15

Would you like a breakdown of why alternate exterior angles are equal or further clarifications?


Here are 5 follow-up questions to explore:

  1. What are alternate exterior angles, and why are they equal when lines are parallel?
  2. How can you confirm whether the solution satisfies the problem?
  3. What happens if the angles are not equal? Are the lines still parallel?
  4. How does this principle apply to other types of angles (e.g., corresponding angles)?
  5. Can this problem be solved graphically or using a different method?

Tip: Always verify your solution by substituting the value of xx back into the expressions for the angles to ensure they are equal!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Geometry
Algebra
Parallel Lines
Alternate Exterior Angles

Formulas

Equation for setting alternate exterior angles equal to each other: 10x = 8x + 30

Theorems

Alternate Exterior Angles Theorem

Suitable Grade Level

Grade 8