The image shows a problem involving parallel lines and transversals. We are asked to find the value of $x$, which represents an angle.

Given Information:

• Lines $l \parallel m \parallel n$ (three parallel lines).
• A transversal cuts through these lines.
• One angle is marked as $145^\circ$, and another is marked as $x^\circ$.

Step-by-Step Solution:

1. Recognize angle relationships:

   • The angle marked $145^\circ$ is on the exterior of the parallel lines, and it forms a pair of supplementary angles with the angle directly across from it on the same line.
   • Since parallel lines are involved, the transversal forms corresponding angles, alternate interior angles, or supplementary angles.

2. Supplementary angle rule:

   • The sum of angles on a straight line is always $180^\circ$.
   • So, the angle $x$ and $145^\circ$ are supplementary because they are on the same transversal at the intersections of line $m$ and line $n$.

3. Solve for $x$:

   • Using the supplementary angle property: $x + 145^\circ = 180^\circ$
   • Subtract $145^\circ$ from both sides: $x = 180^\circ - 145^\circ = 35^\circ$

Thus, the value of $x$ is $35^\circ$.

Let me know if you need further details or have any questions!

Here are 5 related questions you might find helpful:

1. What is the alternate interior angle theorem, and how does it apply here?
2. How can you identify corresponding angles in a similar transversal problem?
3. What is the difference between consecutive interior angles and alternate exterior angles?
4. How would the solution change if the given angle were on the other side of the transversal?
5. Can two angles formed by a transversal and parallel lines be complementary instead of supplementary?

Tip: Always remember that angles on a straight line add up to 180°, which is crucial for transversal problems involving parallel lines.