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The diagram shows three parallel lines \( l \parallel m \parallel n \), with a transversal line crossing them, creating angles \( (6x)^\circ \) and \( 60^\circ \).

Since the lines \( l \), \( m \), and \( n \) are parallel and cut by a transversal, the corresponding angles are equal. The angle labeled \( (6x)^\circ \) is a corresponding angle to the angle labeled \( 60^\circ \).

Thus, we can set up the equation:
\[
6x = 60
\]
Now, solve for \( x \):

\[
x = \frac{60}{6} = 10
\]

Therefore, the value of \( x \) is \( \boxed{10} \).

Would you like any further details or explanations? Here are some follow-up questions related to the problem:

1. How do corresponding angles behave when lines are parallel?
2. What are alternate interior angles, and how do they relate to parallel lines?
3. Can you find any supplementary angles in this figure?
4. How would the solution change if one of the lines were not parallel?
5. How are transversals used to solve real-world problems involving parallel lines?

**Tip:** Always look for corresponding, alternate interior, and exterior angles when working with parallel lines and transversals. These relationships simplify finding unknown angle measures.

Learn how to find the value of x using corresponding angles and parallel lines cut by a transversal. This example demonstrates the Corresponding Angle Theorem where two angles are equal due to the parallel nature of the lines.

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