https://file.aiquickdraw.com/mathbot/file/1725935228700z3fjplbb.jpg

The image shows a transversal cutting through two parallel lines, \( m \parallel n \), with angle expressions \( (8x - 9)^\circ \) and \( (6x + 1)^\circ \).

Since the lines are parallel, the two angles shown in the diagram are alternate interior angles, and therefore, they are equal.

### Step-by-step solution:
1. Set the two angle expressions equal to each other:
   \[
   8x - 9 = 6x + 1
   \]

2. Subtract \( 6x \) from both sides to simplify:
   \[
   2x - 9 = 1
   \]

3. Add 9 to both sides:
   \[
   2x = 10
   \]

4. Divide by 2:
   \[
   x = 5
   \]

### Final answer:
The value of \( x \) is \( 5 \).

Let me know if you'd like more details or have any questions.

### Follow-up questions:
1. What are alternate interior angles, and how do they work with parallel lines?
2. How can you check if two angles are alternate interior angles in a given figure?
3. What are other types of angles formed by a transversal and parallel lines, such as corresponding angles?
4. How does solving linear equations help in geometry problems involving angles?
5. Can you solve for \( x \) if the angles were given as consecutive interior angles instead?

### Tip:
Always verify the properties of angles (alternate, corresponding, etc.) when dealing with parallel lines, as these relationships are key to solving for unknowns.

Given m || n, find the value of x. (8x-9)° and (6x+1)° are the angles formed by a transversal cutting parallel lines m and n.

Learn how to solve for x in a transversal problem where parallel lines are cut by a transversal, forming alternate interior angles. The equation involves setting the angles (8x-9)° and (6x+1)° equal and solving for x. Suitable for Grades 8-10 students.

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