The image shows a problem where two angles are given in terms of $x$ as $(7x - 1)^\circ$ and $(6x - 1)^\circ$. These angles are vertically opposite angles, meaning they are equal.

We can set up the following equation based on the equality of vertically opposite angles:

$7x - 1 = 6x - 1$

Now, let's solve for $x$:

1. Subtract $6x$ from both sides: $7x - 6x - 1 = -1$ $x - 1 = -1$

2. Add 1 to both sides: $x = 0$

Thus, the value of $x$ is $x = 0$.

Would you like further details or have any questions? Here are some related questions to deepen your understanding:

1. What are vertically opposite angles and why are they always equal?
2. What would happen if one angle was slightly modified?
3. How would you solve this problem if the angles weren't opposite but complementary?
4. What is the difference between adjacent and vertically opposite angles?
5. How do we apply angle properties in geometry proofs?

Tip: Always verify if angles are vertically opposite or supplementary when solving angle problems involving lines that intersect.