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To solve for \( x \) in the given problem, we need to use the fact that the lines \( l \) and \( m \) are parallel. When two parallel lines are intersected by a transversal, the corresponding angles are equal.

Here, the corresponding angles are \( x + 6 \) and \( 2x - 36 \).

So, we set them equal to each other:

\[
x + 6 = 2x - 36
\]

Now, solve for \( x \):

1. Subtract \( x \) from both sides:

\[
6 = x - 36
\]

2. Add 36 to both sides:

\[
42 = x
\]

So, the value of \( x \) is \( \boxed{42} \).

Would you like more details or have any questions?

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Here are some related questions to explore:

1. What are corresponding angles in the context of parallel lines and a transversal?
2. Can we use alternate interior angles to solve a similar problem? How?
3. What other angle relationships exist when two parallel lines are intersected by a transversal?
4. How would the solution change if the angles given were alternate exterior angles?
5. What are some real-world applications of parallel lines and transversals?

**Tip:** Always check if angles are corresponding, alternate interior, or alternate exterior when dealing with parallel lines and a transversal—they provide key clues to solving for unknown variables.

If l and m are parallel lines, find the value of x.

Learn how to solve for x in a geometry problem involving parallel lines and a transversal. This problem covers key algebraic and geometric concepts, including the Corresponding Angles Postulate. Suitable for students in Grades 7-9.

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