The problem asks us to find the value of $x$ given that arc $CB$ measures $115^\circ$ and is expressed as $7x - 6$ and arc $AB$ also measures $115^\circ$ and is expressed as $5x + 8$.

1. Problem Description

The problem asks us to find the value of $x$ given that arc $CB$ measures $115^\circ$ and is expressed as $7x - 6$ and arc $AB$ also measures $115^\circ$ and is expressed as $5x + 8$.

2. Solution Steps

Since the measures of the arcs $CB$ and $AB$ are both equal to $115^\circ$, we can set the expressions for their measures equal to each other.

$7x - 6 = 5x + 8$

Now, we solve for $x$.

Subtract $5x$ from both sides:

$7x - 5x - 6 = 5x - 5x + 8$

$2x - 6 = 8$

Add 6 to both sides:

$2x - 6 + 6 = 8 + 6$

$2x = 14$

Divide both sides by 2:

$\frac{2x}{2} = \frac{14}{2}$

$x = 7$

3. Final Answer

$x = 7$