1. **Problem statement:** Given two parallel lines $m \parallel n$ and a transversal line intersecting them, find the value of angle $x$ when the angle on the bottom line is $109^\circ$. 2. **Key concept:** When a transversal crosses two parallel lines, alternate interior angles are equal. 3. **Apply the rule:** The angle $x$ on the top line and the $109^\circ$ angle on the bottom line are alternate interior angles. 4. **Therefore,** $$x = 109^\circ$$ 5. **Answer:** The value of $x$ is $109$ degrees.