1. **State the problem:** We have two parallel lines $a$ and $b$ cut by a transversal. One angle formed is $55^\circ$ and we need to find the value of $x$ which is the angle vertically opposite or corresponding to the $55^\circ$ angle. 2. **Recall the properties:** When two parallel lines are cut by a transversal, corresponding angles are equal, alternate interior angles are equal, and vertically opposite angles are equal. 3. **Identify the relationship:** The angle $55^\circ$ and angle $x$ are alternate interior angles because they lie on opposite sides of the transversal and between the two parallel lines. 4. **Apply the property:** Since $a \parallel b$, alternate interior angles are equal, so $$x = 55^\circ$$ 5. **Conclusion:** The value of $x$ is $55$ degrees.