1. **Stating the problem:** We are given two intersecting lines forming angles, with one angle labeled $x$ and the corresponding angle on the opposite side labeled $72^\circ$. We need to find the value of $x$. 2. **Key concept:** When two lines intersect, opposite (vertical) angles are equal. 3. **Applying the rule:** Since $x$ and $72^\circ$ are vertical angles, they must be equal. 4. **Conclusion:** Therefore, $x = 72^\circ$. **Final answer:** $x = 72^\circ$