In the image provided, there is a diagram with intersecting lines and marked angles, including the expressions and values for the angles. Here's the information extracted from the diagram:

• One angle is labeled as $107^\circ$.
• Another angle is labeled as $55^\circ$.
• A third angle is expressed as $(4 - 2x)^\circ$.

Approach:

We can use the properties of intersecting lines (particularly, vertically opposite angles) and the fact that the sum of angles on a straight line is $180^\circ$.

Step 1: Identify vertical angles

• The angle opposite $107^\circ$ is also $107^\circ$.
• The angle opposite $55^\circ$ is also $55^\circ$.

Step 2: Apply angle sum on a straight line

On the straight line containing the $107^\circ$ angle and $(4 - 2x)^\circ$, their sum should equal $180^\circ$.

Thus, we can set up the equation: $107 + (4 - 2x) = 180$

Now, let's solve for $x$.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can solve this equation manually:

$107 + (4 - 2x) = 180$

Subtract 107 from both sides:

$4 - 2x = 180 - 107$ $4 - 2x = 73$

Now subtract 4 from both sides:

$-2x = 73 - 4$ $-2x = 69$

Finally, divide by -2:

$x = \frac{69}{-2} = -34.5$

Let me know if you need further clarifications!

Related questions:

1. What are vertically opposite angles, and how do they relate to intersecting lines?
2. How do you find unknown angles when given expressions for them?
3. What is the sum of angles on a straight line?
4. Can angles be negative, and if so, what does that represent?
5. How do you solve linear equations involving variables in geometric contexts?

Tip: Always check if your angles make sense logically in the context of the figure when solving!