1. **State the problem:** We are given two intersecting lines forming vertical angles. One angle measures $81.7^\circ$ and the angle vertically opposite to it is labeled $h$. We need to find the value of $h$. 2. **Recall the property of vertical angles:** Vertical angles are the angles opposite each other when two lines intersect. They are always equal. 3. **Apply the property:** Since $h$ and $81.7^\circ$ are vertical angles, we have $$h = 81.7^\circ$$ 4. **Conclusion:** The value of $h$ is $81.7^\circ$.