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.