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In the image, you're given a problem where two lines, \( A \) and \( B \), are parallel, and you are asked to find the value of \( x \) that makes the alternate exterior angles equal.

### Given:
- One angle is \( 10x \).
- The other angle is \( 8x + 30 \).

### Since the lines are parallel (\( A \parallel B \)), the alternate exterior angles are congruent, meaning:

\[
10x = 8x + 30
\]

### Step-by-step solution:
1. Start with the equation \( 10x = 8x + 30 \).
2. Subtract \( 8x \) from both sides to isolate \( x \):

\[
10x - 8x = 30
\]

\[
2x = 30
\]

3. Divide both sides by 2 to solve for \( x \):

\[
x = 15
\]

Thus, the value of \( x \) is \( 15 \).

Would you like a detailed breakdown of this solution or any additional clarifications?

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Here are five relative questions that expand on this topic:
1. What are alternate exterior angles, and why are they congruent when lines are parallel?
2. How do we identify alternate exterior angles in different diagrams?
3. What happens if the lines are not parallel in terms of alternate exterior angles?
4. How do other angle relationships (like corresponding or alternate interior angles) work with parallel lines?
5. What are the methods to prove lines are parallel using angles?

### Tip: 
Remember, alternate exterior angles are always congruent when the lines involved are parallel, making them a useful tool for proving parallelism.

Follow the steps below to find the value of x that makes A parallel to B, where one angle is 10x and the other angle is 8x + 30. Set the alternate exterior angles equal to each other.

Learn how to solve for x by setting alternate exterior angles equal in a problem involving parallel lines. Using the equation 10x = 8x + 30, this problem is suitable for students in Grades 7-9 and covers key concepts from geometry and algebra.

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