The problem provides the measures of the six interior angles of a hexagon in terms of $x$. The task is to find the value of $x$. The given angles are $107^\circ$, $(2x)^\circ$, $150^\circ$, $95^\circ$, $(2x-15)^\circ$, and $123^\circ$.

1. Problem Description

The problem provides the measures of the six interior angles of a hexagon in terms of $x$. The task is to find the value of $x$. The given angles are $107^\circ$, $(2x)^\circ$, $150^\circ$, $95^\circ$, $(2x-15)^\circ$, and $123^\circ$.

2. Solution Steps

The sum of the interior angles of a polygon with $n$ sides is given by the formula:

$$S = (n-2) \times 180^\circ$$

For a hexagon, $n=6$, so the sum of the interior angles is:

$$S = (6-2) \times 180^\circ = 4 \times 180^\circ = 720^\circ$$

Now, we can write an equation by summing the given angles and setting it equal to $720^\circ$:

$$107 + 2x + 150 + 95 + (2x-15) + 123 = 720$$

Combine the constant terms:

$$107 + 150 + 95 - 15 + 123 = 460$$

So, the equation becomes:

$$460 + 2x + 2x = 720$$

$$460 + 4x = 720$$

Subtract 460 from both sides:

$$4x = 720 - 460$$

$$4x = 260$$

Divide by 4:

$$x = \frac{260}{4}$$

$$x = 65$$

3. Final Answer

The value of $x$ is

6

5. So, the answer is B. 65.