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In the given image, we have two lines, \( m \) and \( n \), which are parallel, and a transversal that crosses them forming an angle of \( 160^\circ \) with line \( n \). The angle marked as \( x^\circ \) on the image corresponds to the alternate interior angle relative to the \( 160^\circ \) angle on the other side of the transversal. 

By the Alternate Interior Angles Theorem, which states that alternate interior angles are equal when two lines are parallel and cut by a transversal, we can determine that:

\[
x = 160^\circ
\]

Hence, the value of \( x \) is \( 160^\circ \).

Would you like more details or do you have any other questions on this topic? Here are some follow-up questions you might consider:

1. How would the solution change if the angle was not given and only the relationship between the lines was provided?
2. What happens to the angles if the lines \( m \) and \( n \) were not parallel?
3. How does the Corresponding Angles Postulate apply to parallel lines cut by a transversal?
4. Can you find the angle between the transversal and line \( m \) using the given information?
5. What are supplementary and complementary angles in the context of parallel lines and a transversal?

Tip: Remember, when dealing with transversals and parallel lines, always consider the various angle relationships like corresponding angles, alternate interior angles, and consecutive interior angles.

Given m || n, find the value of x in the diagram where angle 160° is provided.

Learn how to determine the value of x using the Alternate Interior Angles Theorem with parallel lines and a transversal. This geometry problem focuses on angle relationships formed by parallel lines cut by a transversal. Suitable for students in Grades 8-10.

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