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In this problem, we are given two parallel lines \( m \parallel n \), cut by a transversal \( t \). The two given angles, \( (5x + 8)^\circ \) and \( (6x - 18)^\circ \), are alternate interior angles. Since the lines are parallel, alternate interior angles are congruent. Thus, we can set the expressions for these angles equal to each other:

\[
5x + 8 = 6x - 18
\]

### Solving for \( x \):

1. Subtract \( 5x \) from both sides:
   \[
   8 = x - 18
   \]

2. Add 18 to both sides:
   \[
   26 = x
   \]

Thus, the value of \( x \) is:

\[
x = 26
\]

Would you like more details or have any other questions?

### Related questions:
1. What is the definition of alternate interior angles?
2. How would the equation change if the angles were supplementary instead of congruent?
3. Can alternate exterior angles be used in a similar problem setup? Why or why not?
4. How do parallel lines affect angle relationships when a transversal is introduced?
5. If the angles were corresponding instead, what equation would be set up?

### Tip:
Always remember that for parallel lines cut by a transversal, corresponding angles, alternate interior angles, and alternate exterior angles are congruent.

Given m parallel to n, find the value of x for angles (5x + 8)° and (6x - 18)° being alternate interior angles.

Learn how to solve for x in a geometry problem involving two parallel lines and a transversal, using the Alternate Interior Angles Theorem. This step-by-step solution covers key concepts in algebra and geometry for students in Grades 8-10.

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