https://file.aiquickdraw.com/mathbot/file/17289998473081db6ujz6.jpg

The problem is asking to find the value of \( x \) such that line \( l \) is parallel to line \( m \), and to state the converse used.

From the image, we see two angles:
- \( (9x + 37)^\circ \) 
- \( (14x - 23)^\circ \)

These angles appear to be **corresponding angles** since they are on the same side of the transversal and in the same relative positions.

### Step-by-step solution:

1. **Corresponding Angles Postulate (Converse):** 
   - If two corresponding angles are equal, then the two lines are parallel.
   - So, we can set the angles equal to each other:
   \[
   9x + 37 = 14x - 23
   \]

2. **Solve for \( x \):**
   \[
   9x + 37 = 14x - 23
   \]
   Subtract \( 9x \) from both sides:
   \[
   37 = 5x - 23
   \]
   Add 23 to both sides:
   \[
   60 = 5x
   \]
   Divide both sides by 5:
   \[
   x = 12
   \]

### Converse Used:
The converse of the **Corresponding Angles Postulate** states that if two corresponding angles are congruent, then the lines are parallel.

### Final Answer:
- The value of \( x \) is 12.
- The converse used is the **Corresponding Angles Postulate**.

---

Would you like further details or explanations? Here are some related questions:

1. What are corresponding angles, and why are they important for parallel lines?
2. What other angle relationships (such as alternate interior angles) could help prove lines are parallel?
3. How do you verify that two lines are parallel using a transversal and angle relationships?
4. Can the same problem be solved using a different postulate or theorem?
5. What are other converses related to angle postulates in geometry?

**Tip:** When working with parallel lines and a transversal, remember to check the type of angles formed (corresponding, alternate interior, etc.) to determine relationships.

Find the value of x so that l || m. State the converse used. The angles given are (9x + 37)° and (14x - 23)°.

Learn how to solve for x in a geometry problem involving parallel lines and corresponding angles. Given angles (9x + 37)° and (14x - 23)°, find x and understand the converse of the Corresponding Angles Postulate. Suitable for students in Grades 8-10.

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