https://file.aiquickdraw.com/mathbot/file/1725434175507yf4dppr7.jpg

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!

Find the value of x based on the given intersecting lines and angle measures.

Determine the value of x in this geometry problem involving intersecting lines and given angle measures. This problem covers key geometric concepts, including linear pairs and vertically opposite angles. Suitable for students in Grades 6-8.

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