The image shows a diagram with several intersecting lines, creating multiple angles. Based on the given information, we are tasked with finding the value of $x$.

Step 1: Identify the angles

• The angle labeled $118^\circ$ is highlighted in green.
• The angle labeled $106^\circ$ is highlighted in orange.
• The angle labeled $x$ is highlighted in blue.

Step 2: Analyze the relationships between angles

• Since the lines are intersecting, we can use angle relationships such as vertical angles (which are equal) and linear pairs (which add up to $180^\circ$).

From the diagram:

1. The $118^\circ$ angle and the angle adjacent to it on the same straight line should form a linear pair, summing to $180^\circ$. Therefore, the angle adjacent to $118^\circ$ is $180^\circ - 118^\circ = 62^\circ$.

2. The $106^\circ$ angle forms a linear pair with the angle next to it, which means the adjacent angle is $180^\circ - 106^\circ = 74^\circ$.

3. Since $x$ is vertically opposite the angle that forms a linear pair with $106^\circ$, it should be equal to $74^\circ$.

Therefore, the value of $x$ is $74^\circ$.

If you have any questions or would like a more detailed explanation, feel free to ask! Here are some related questions for further practice:

1. What is the measure of the angle opposite to $118^\circ$?
2. How do you find the measure of an angle that forms a linear pair with a given angle?
3. What is the relationship between vertically opposite angles?
4. How can you confirm the correctness of angle measures in a geometric diagram?
5. What other angle relationships can be identified in a complex intersecting line diagram?

Tip: Remember that in intersecting lines, vertically opposite angles are always equal, which can simplify finding unknown angles!