https://file.aiquickdraw.com/mathbot/file/1726755127690y1kapkqd.jpg

To solve for \( x \) in this diagram, we can use the properties of parallel lines and angles.

### Key observation:
- The lines \( m \) and \( n \) are parallel (\( m \parallel n \)).
- The two angles given, \( (10x + 8)^\circ \) and \( (7x + 2)^\circ \), are **corresponding angles** since they are formed by a transversal intersecting parallel lines. For corresponding angles, they are always equal.

### Setting up the equation:
\[
10x + 8 = 7x + 2
\]

### Solving for \( x \):

1. Subtract \( 7x \) from both sides:
   \[
   10x - 7x + 8 = 2
   \]
   \[
   3x + 8 = 2
   \]

2. Subtract 8 from both sides:
   \[
   3x = 2 - 8
   \]
   \[
   3x = -6
   \]

3. Divide both sides by 3:
   \[
   x = \frac{-6}{3} = -2
   \]

Thus, the value of \( x \) is \( -2 \).

Do you want more details, or do you have any further questions?

### Related questions:
1. What are the other types of angle relationships in parallel lines cut by a transversal?
2. How do we solve equations with variables on both sides?
3. What are alternate interior angles, and how are they related in parallel lines?
4. Can we have multiple transversal lines intersecting two parallel lines?
5. What is the sum of the angles on a straight line?

### Tip:
Always remember that corresponding angles formed by a transversal cutting two parallel lines are congruent!

Learn how to solve for x when given two parallel lines and a transversal. The problem focuses on corresponding angles and uses simple algebra to find x = -2. Suitable for students in Grades 8-10.

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