1. **Problem statement:** We have two parallel lines cut by a transversal, creating angles labeled $x^\circ$, $y^\circ$, $z^\circ$, $110^\circ$, and $50^\circ$. We need to find the value of $x$ and give a geometrical reason. 2. **Key fact:** When two parallel lines are cut by a transversal, corresponding angles are equal. 3. **Identify corresponding angles:** The angle $x^\circ$ on the upper parallel line corresponds to the angle $110^\circ$ on the lower parallel line because they are in the same relative position at the intersection with the transversal. 4. **Therefore,** by the Corresponding Angles Postulate: $$x = 110$$ 5. **Geometrical reason:** Corresponding angles formed by a transversal cutting two parallel lines are equal. **Final answer:** $x = 110^\circ$