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If I || m, classify the marked angle pair and give their relationship, then solve for x.

The diagram shows two parallel lines \( l \parallel m \) with two intersecting transversal lines, creating two marked angles: 

- \( (18x - 44)^\circ \)
- \( (8x - 10)^\circ \)

These angles are positioned as alternate interior angles, given that the lines \( l \parallel m \) and the transversal cutting through both creates this relationship. For parallel lines, alternate interior angles are congruent. Therefore, we can set the two angles equal to each other:

\[
18x - 44 = 8x - 10
\]

### Step 1: Solve for \( x \)
First, subtract \( 8x \) from both sides:

\[
18x - 8x - 44 = -10
\]

This simplifies to:

\[
10x - 44 = -10
\]

Next, add 44 to both sides:

\[
10x = 34
\]

Now, divide both sides by 10:

\[
x = \frac{34}{10} = 3.4
\]

So, \( x = 3.4 \).

### Step 2: Verify the angles
Substitute \( x = 3.4 \) back into the expressions for the angles:

- First angle: \( 18x - 44 = 18(3.4) - 44 = 61.2 - 44 = 17.2^\circ \)
- Second angle: \( 8x - 10 = 8(3.4) - 10 = 27.2 - 10 = 17.2^\circ \)

Since both angles are equal, the solution \( x = 3.4 \) is correct.

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Do you need more details or have any questions?

### Related Questions:
1. What are alternate exterior angles, and how do they differ from alternate interior angles?
2. How do corresponding angles behave when lines are parallel?
3. How can you prove two lines are parallel using angles formed by a transversal?
4. What are the properties of consecutive interior angles for parallel lines?
5. How would the problem change if the lines were not parallel?

### Tip:
Remember, if two lines are parallel, alternate interior angles will always be congruent!

Learn how to solve for x in a problem involving parallel lines and alternate interior angles. This step-by-step solution covers the Alternate Interior Angles Theorem and shows how to verify the solution. Suitable for students in Grades 8-10.

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