https://file.aiquickdraw.com/mathbot/file/17273635020015mlvlh8l.jpg

In the image, we are given two parallel lines \( m \parallel n \), and a transversal intersects them, forming two angles:

1. \( (9x - 8)^\circ \)
2. \( (4x + 22)^\circ \)

Since the lines are parallel, these two angles are *alternate interior angles*, which means they are equal. Therefore, we can set the two expressions for the angles equal to each other:

\[
9x - 8 = 4x + 22
\]

### Solving for \( x \):

1. Subtract \( 4x \) from both sides:
\[
9x - 4x - 8 = 22
\]
\[
5x - 8 = 22
\]

2. Add 8 to both sides:
\[
5x = 30
\]

3. Divide both sides by 5:
\[
x = 6
\]

Thus, the value of \( x \) is \( \boxed{6} \).

---

Would you like a detailed explanation on why alternate interior angles are equal? Here are some follow-up questions for practice:

1. What are the properties of alternate interior angles?
2. How do you determine whether two lines are parallel using a transversal?
3. What other angle relationships exist when a transversal intersects two parallel lines?
4. If \( x = 6 \), what is the measure of each angle in the diagram?
5. How would the solution change if the lines were not parallel?

**Tip:** When solving equations with angles, always check if the lines involved are parallel, as this determines angle relationships.

Learn how to solve for x in a problem involving parallel lines and a transversal. The alternate interior angle theorem is applied, leading to an equation that solves for x. Suitable for students in Grades 7-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation