https://file.aiquickdraw.com/mathbot/file/1725311048023us45av1z.jpg

In the image, lines \( m \) and \( n \) are parallel, and a transversal crosses these lines, creating two angles: \( x^\circ \) and \( 42^\circ \).

Because \( m \) and \( n \) are parallel, the angles formed on the same side of the transversal are **corresponding angles**. Corresponding angles are equal when two lines are parallel. Therefore, the value of \( x \) is equal to \( 42^\circ \).

So, the correct answer is \( x = 42^\circ \).

Would you like more details on this? Here are some related questions to consider:

1. What are alternate interior angles, and how do they relate to parallel lines?
2. How would you calculate \( x \) if the transversal made different angles with the parallel lines?
3. Can you explain the concept of vertical angles in this diagram?
4. How can we use the properties of parallel lines to solve for unknown angles?
5. What happens if the lines \( m \) and \( n \) were not parallel?

**Tip:** When working with parallel lines and a transversal, always check for corresponding, alternate interior, or alternate exterior angles to find unknown values.

Explore how to solve for unknown angles using corresponding angles formed by parallel lines and a transversal. Learn the properties of parallel lines and their relationship with transversals in geometry problems. Suitable for Grades 7-9.

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