1. **State the problem:** We are given two parallel lines $a$ and $b$ cut by a transversal, with an angle of $155^\circ$ adjacent to angle $x$. We need to find the value of $x$. 2. **Recall the properties:** When two parallel lines are cut by a transversal, consecutive interior angles are supplementary, meaning their measures add up to $180^\circ$. 3. **Identify the relationship:** Since $a \parallel b$, angle $x$ and the $155^\circ$ angle are consecutive interior angles. 4. **Set up the equation:** $$x + 155^\circ = 180^\circ$$ 5. **Solve for $x$:** $$x = 180^\circ - 155^\circ$$ $$x = 25^\circ$$ 6. **Conclusion:** The value of $x$ is $25^\circ$.