https://r2.erweima.ai/mathbot/image/1726500141401ntfeuko2.jpg

The image provides two angles and asks to solve for \( x \) to make lines \( A \) and \( B \) parallel (denoted \( A \parallel B \)).

### Step-by-step solution:
To solve this problem, we need to understand that when two lines are parallel, the corresponding angles are equal.

- The given angle on the right (upper angle) is 80°.
- The angle on the left is labeled as \( 4x + 8 \).

Since \( A \parallel B \), these two angles must be equal because they are corresponding angles formed by a transversal. So, we can set up the equation:

\[
4x + 8 = 80
\]

### Solve for \( x \):
1. Subtract 8 from both sides:
   \[
   4x = 80 - 8
   \]
   \[
   4x = 72
   \]
   
2. Divide both sides by 4:
   \[
   x = \frac{72}{4}
   \]
   \[
   x = 18
   \]

Thus, the value of \( x \) is **18**.

### Final Answer:
\[
x = 18
\]

Would you like further details or have any questions?

Here are some related questions you might want to explore:
1. What are alternate interior angles, and how are they different from corresponding angles?
2. How do you prove two lines are parallel using angles?
3. Can we use the same method if the transversal forms supplementary angles?
4. What happens if the given angles form a different type of pair (e.g., alternate exterior angles)?
5. How can you apply the same principle when working with polygons?

**Tip**: When solving for parallel lines, always check if you're dealing with corresponding, alternate interior, or supplementary angles, as each can have different relationships.

Solve for x to make A || B. Given angles: (4x + 8)° and 80°.

This problem involves solving for x to make lines A and B parallel by using the Corresponding Angles Postulate. Given that the angles are (4x + 8)° and 80°, students will learn to set up and solve the equation to find the value of x. Suitable for students in Grades 7-9.

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