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In the image provided, you are given two parallel lines \( m \parallel n \), and two angles formed by a transversal intersecting the parallel lines. The expressions for the two angles are \( (9x - 10)^\circ \) and \( (8x - 14)^\circ \). Since the lines are parallel and these angles are on opposite sides of the transversal, they are alternate interior angles, which means they are equal.

We can set up the equation:

\[
9x - 10 = 8x - 14
\]

Now, let's solve for \( x \):

1. Subtract \( 8x \) from both sides:

\[
9x - 8x - 10 = -14
\]

\[
x - 10 = -14
\]

2. Add 10 to both sides:

\[
x = -14 + 10
\]

\[
x = -4
\]

Thus, the value of \( x \) is \( -4 \).

Would you like further explanation or have any questions?

Here are 5 related questions:
1. What are alternate interior angles?
2. Why are alternate interior angles equal when lines are parallel?
3. Can alternate interior angles be used in non-parallel line scenarios?
4. What other angle relationships exist when a transversal intersects parallel lines?
5. How does changing the transversal's slope affect the angles formed?

**Tip:** In geometry, recognizing angle relationships like alternate interior angles can simplify solving for unknowns when parallel lines are involved.

Solve for x in the given diagram where two parallel lines are cut by a transversal, forming alternate interior angles. Using algebra and the Alternate Interior Angles Theorem, find the correct value for x in the equation (9x - 10)° = (8x - 14)°. Suitable for students in Grades 8-10.

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