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In the given image, you are asked to find the value of \( x \) given that lines \( m \parallel n \) (lines \( m \) and \( n \) are parallel).

You are provided with two angles:

1. \( (6x + 30)^\circ \)
2. \( (8x - 10)^\circ \)

These angles appear to be corresponding angles because they are on the same side of the transversal and between the two parallel lines. Since corresponding angles are congruent (equal) when lines are parallel, we can set the two expressions equal to each other:

\[
6x + 30 = 8x - 10
\]

Now, let's solve for \( x \).

### Steps:
1. Subtract \( 6x \) from both sides:
   \[
   30 = 2x - 10
   \]

2. Add 10 to both sides:
   \[
   40 = 2x
   \]

3. Divide both sides by 2:
   \[
   x = 20
   \]

Thus, the value of \( x \) is \( 20 \).

Would you like further details or have any questions?

Here are 5 related questions for further practice:
1. What are corresponding angles and how do they relate to parallel lines?
2. Can you calculate the actual angle measures using \( x = 20 \)?
3. How would the solution change if the lines \( m \) and \( n \) were not parallel?
4. What is the relationship between alternate interior angles in parallel lines?
5. How can you prove two lines are parallel using angle relationships?

**Tip:** Always check if lines are parallel in geometry problems to use angle congruence properties effectively!

Learn how to solve for x using the corresponding angles theorem, where two angles are given as 6x + 30° and 8x - 10° with parallel lines. This problem involves solving a linear equation and understanding angle relationships in parallel lines. Suitable for students in Grades 8-10.

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