It seems like you're describing a situation where two lines, $m \parallel n$, are parallel, and angles formed between these lines are given as $(7x - 2)^\circ$ and $(8x - 23)^\circ$. You want to find the value of $x$.

When two lines are parallel, the corresponding angles are equal. This means we can set up an equation where the two angle expressions are equal:

$7x - 2 = 8x - 23$

Now, let's solve for $x$:

1. First, subtract $7x$ from both sides:

$-2 = x - 23$

2. Now, add 23 to both sides:

$21 = x$

Thus, the value of $x$ is $21$.

Would you like further clarification or more details? Here are some related questions that could deepen your understanding:

1. How does the property of corresponding angles relate to parallel lines?
2. What are alternate interior angles, and how are they used in parallel line geometry?
3. Can you explain the difference between corresponding angles and supplementary angles?
4. What is the significance of transversals in geometry?
5. How do we solve for $x$ when we have angle relationships with parallel lines and a transversal?

Tip: Always check whether the angles are corresponding, alternate, or supplementary before setting up equations!