Step 1: Convert exterior angles into interior angles

Each marked angle is an exterior angle of $130^\circ$.

So, corresponding interior angle:

$180^\circ - 130^\circ = 50^\circ$

Thus, the two relevant interior angles are $50^\circ$ each.

Step 2: Analyze the line inclinations

The upper slanted line makes an angle of $50^\circ$ with the middle line.

Similarly, the lower slanted line also forms a related $50^\circ$ angle, but on the opposite side.

Using the geometry of the intersecting lines, the acute angle between the two slanted segments becomes:

$ x = 50^\circ - 20^\circ $

Step 3: Calculate $x$

$ x = 30^\circ $

Final Answer:

$\boxed{30^\circ}$