This image shows a pair of parallel lines cut by a transversal, creating angles. We are given one angle as $(12x - 8)^\circ$ and another as $100^\circ$. These angles are corresponding angles, which means they are equal.

To solve for $x$, we set the two angles equal to each other:

$12x - 8 = 100$

Now, let's solve for $x$:

1. Add 8 to both sides: $12x = 108$

2. Divide by 12: $x = \frac{108}{12} = 9$

So, $x = 9$.

Would you like a detailed explanation of corresponding angles, or do you have any questions about this?

Here are 5 related questions for further practice:

1. What are alternate interior angles in a transversal problem?
2. How do you solve for $x$ if the angles are supplementary?
3. What happens if the angles are alternate exterior angles?
4. How can we calculate the value of $x$ if we have vertical angles?
5. How do you determine the relationship between interior and exterior angles?

Tip: When dealing with parallel lines and a transversal, identifying angle relationships (like corresponding, alternate interior, or vertical angles) helps solve for unknowns easily.