In the given figure, we have a line intersecting two parallel lines, creating several angles. The angle labeled $136^\circ$ is formed on one side of the transversal, and we are asked to find the value of $x^\circ$, which is an angle formed on the other side.

Step-by-step solution:

1. The two lines are parallel, and the transversal cuts through them. This creates pairs of corresponding angles, alternate interior angles, and supplementary angles.
2. The angle labeled $136^\circ$ and the angle $x^\circ$ are alternate interior angles. According to the alternate interior angle theorem, alternate interior angles between two parallel lines are equal.

Thus, $x^\circ = 136^\circ$.

The value of $x$ is therefore 136 degrees.

Would you like a more detailed explanation or have any questions? Here are five related questions you could explore further:

1. What are alternate interior angles, and why are they always equal for parallel lines?
2. How would the solution change if the lines were not parallel?
3. What is the difference between alternate interior angles and corresponding angles?
4. Can you list other angle relationships created by a transversal cutting through parallel lines?
5. How would you calculate the angle if only the exterior angle was given?

Tip: Always look for relationships like alternate interior angles, corresponding angles, and supplementary angles when dealing with parallel lines and a transversal.