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This problem involves finding the value of \( x \) in the context of parallel lines cut by a transversal.

### Given Information:
- Two parallel lines \( m \parallel n \) are cut by a transversal.
- The angles formed by the intersection of the transversal with the parallel lines are:
  - \( (4x - 8)^\circ \)
  - \( (7x - 20)^\circ \)

### Solution Outline:
Since \( m \parallel n \), these angles are **corresponding angles**, and corresponding angles are congruent when parallel lines are cut by a transversal. Therefore, we can set the two angles equal to each other:

\[
4x - 8 = 7x - 20
\]

### Step-by-Step Solution:

1. **Set up the equation:**
   \[
   4x - 8 = 7x - 20
   \]

2. **Simplify by subtracting \( 4x \) from both sides:**
   \[
   -8 = 3x - 20
   \]

3. **Add 20 to both sides:**
   \[
   12 = 3x
   \]

4. **Solve for \( x \):**
   \[
   x = \frac{12}{3} = 4
   \]

Thus, the value of \( x \) is \( \boxed{4} \).

Would you like further details or have any questions? Here are 5 related questions to explore the concept more:

1. What are corresponding angles, and why are they congruent when lines are parallel?
2. How would the solution change if the angles were supplementary instead of congruent?
3. What is the significance of parallel lines in this type of geometry problem?
4. How do you verify if two lines are parallel in a geometry problem like this?
5. Can you derive the value of \( x \) if the transversal cuts the lines at different angles?

**Tip:** Remember that when solving for \( x \) in geometry problems involving parallel lines and transversals, always check whether the angles are congruent or supplementary depending on their position.

Given m || n, find the value of x. The angles formed are (4x - 8)° and (7x - 20)°.

Solve for x in the problem where two parallel lines are cut by a transversal, forming angles (4x - 8)° and (7x - 20)°. Learn how to apply the Corresponding Angles Theorem to find the value of x. Suitable for students in Grades 8-10.

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