https://file.aiquickdraw.com/mathbot/file/1726156629136qewensag.jpg

The image is asking to solve for \(x\) by setting the two alternate exterior angles equal to each other. The given angles are:

- \( 10x \) (on the left side)
- \( 8x + 30 \) (on the right side)

Since these are alternate exterior angles and lines \( A \) and \( B \) are parallel, we can set them equal:

\[
10x = 8x + 30
\]

To solve for \(x\):

1. Subtract \( 8x \) from both sides:
\[
10x - 8x = 30
\]
\[
2x = 30
\]

2. Divide both sides by 2:
\[
x = \frac{30}{2} = 15
\]

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

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

Here are some related questions:
1. How do alternate exterior angles behave with parallel lines?
2. What are the properties of parallel lines and transversals?
3. What are the other types of angle pairs formed by a transversal?
4. How would the problem change if the angles were supplementary instead of equal?
5. How can we verify if lines are parallel using angles?

**Tip:** Always remember that when two lines are cut by a transversal, alternate exterior angles are equal when the lines are parallel.

Follow the steps below to find the value of x that makes A parallel to B. The angles given are 10x and 8x + 30. Set the alternate exterior angles equal to each other.

Learn how to solve for x using alternate exterior angles to prove that two lines are parallel. In this problem, the angles are 10x and 8x + 30, and we use basic algebra to find x = 15. Suitable for students in Grades 8-10.

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