This problem involves parallel lines ($m \parallel n$) and a transversal, creating angles. Since $m \parallel n$, we can use the properties of corresponding and supplementary angles.

Steps to solve:

1. Identify the relationship between the angles:

   • The given angle is $118^\circ$.
   • The angle $x^\circ$ is on the opposite side of the transversal, forming a linear pair with $118^\circ$.
   • Linear pairs are supplementary, meaning their sum is $180^\circ$.

2. Set up the equation: $118^\circ + x^\circ = 180^\circ$

3. Solve for $x$: $x = 180^\circ - 118^\circ = 62^\circ$

Final Answer:

$x = 62^\circ$

Would you like a detailed explanation of the angle relationships or a review of supplementary angles?

Related Questions:

1. What are corresponding angles and how are they related in parallel lines?
2. How do linear pairs help in solving angle problems?
3. Can vertical angles be used in this problem? Why or why not?
4. What are some real-life applications of parallel lines and transversal concepts?
5. How would the problem change if the transversal was not intersecting parallel lines?

Tip:

Always check for the relationships between angles (e.g., corresponding, alternate interior, supplementary) when working with parallel lines and a transversal.