To solve for the angle $x$ in this problem, let’s go through the steps.

Since the lines $r$ and $s$ are parallel and both are intersected by the transversal $t$, we know certain angle relationships apply.

1. Identify the Corresponding Angles: The angle labeled $135^\circ$ is an exterior angle to the upper intersection point of line $r$ and transversal $t$.
2. Use Alternate Interior Angles: Because $r$ and $s$ are parallel, the angle labeled $135^\circ$ has a corresponding angle on line $s$ which is equal to it by the alternate interior angles theorem. This means angle $x$ is also $135^\circ$.

Conclusion: The measure of angle $x$ is $135^\circ$.

Would you like further details on alternate interior angles or any other related concepts?

Here are five related questions you might find useful:

1. How do corresponding angles work in parallel lines?
2. What is the alternate interior angles theorem?
3. Why do parallel lines create equal corresponding and alternate interior angles?
4. How can we prove that two angles are equal when intersected by a transversal?
5. How do exterior angles relate to parallel lines?

Tip: In geometry, identifying parallel lines and transversals is key to finding angle relationships!