https://file.aiquickdraw.com/mathbot/file/17264417253836qwgoj0r.jpg

In the image, we are dealing with two parallel lines \( m \parallel n \) that are intersected by a transversal line. The angle marked as \( x^\circ \) is on the same side of the transversal as the angle marked \( 142^\circ \). This means that these two angles are **same-side interior angles**, which are supplementary when two lines are parallel.

To find the value of \( x \), we can use the fact that:

\[
x + 142^\circ = 180^\circ
\]

Solving for \( x \):

\[
x = 180^\circ - 142^\circ
\]
\[
x = 38^\circ
\]

Thus, \( x = 38^\circ \).

Would you like further details on how transversal angles work or more examples of similar problems?

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Here are 5 related questions:
1. What are alternate interior angles, and how are they used in problems like this?
2. How do corresponding angles relate when two parallel lines are cut by a transversal?
3. Can you identify the exterior angles in this type of transversal diagram?
4. What is the difference between consecutive interior angles and alternate exterior angles?
5. How would the angle relationships change if the lines were not parallel?

**Tip**: Always remember that when parallel lines are cut by a transversal, several angle pairs such as corresponding, alternate interior, and consecutive interior angles are formed. These relationships help determine unknown angles.

Solve for x using the same-side interior angles theorem with two parallel lines and a transversal. Given that one angle is 142°, find the supplementary angle for x. Suitable for students in Grades 8-10.

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