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The image shows two parallel lines \( p \) and \( q \) cut by a transversal \( m \). We are given two expressions for the angles on either side of the transversal: \( (2x - 3)^\circ \) on the left and \( (x + 9)^\circ \) on the right. The question asks for the value of \( x \) that would prove \( p \parallel q \).

### Solution:

For \( p \parallel q \), the corresponding angles formed by the transversal must be equal. Thus, the angles given by \( (2x - 3)^\circ \) and \( (x + 9)^\circ \) must be equal.

We can set up the following equation:
\[
2x - 3 = x + 9
\]

Now, solve for \( x \):

1. Subtract \( x \) from both sides:
   \[
   2x - x - 3 = 9
   \]
   This simplifies to:
   \[
   x - 3 = 9
   \]

2. Add 3 to both sides:
   \[
   x = 12
   \]

Thus, the value of \( x \) that makes the lines \( p \parallel q \) is \( \boxed{12} \).

### Answer: 12

Would you like more details on this or have any other questions?

Here are some related questions for further practice:
1. What is the corresponding angle theorem in geometry?
2. How do you solve for \( x \) when two alternate interior angles are equal?
3. What conditions must be met for two lines to be parallel when cut by a transversal?
4. What is the relationship between corresponding and alternate angles?
5. How can you determine if two lines are parallel using only angle measures?

**Tip**: When working with parallel lines and transversals, remember that corresponding angles are always equal when the lines are parallel.

What value of x would prove that p is parallel to q? Given that the angles are (2x - 3)° and (x + 9)°, respectively.

Learn how to find the value of x that proves two lines are parallel using the corresponding angles theorem. This problem involves setting two angles equal to each other: (2x - 3)° and (x + 9)°. Suitable for students in Grades 8-10.

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