1. **Stating the problem:** We are given multiple geometric figures with angles and side lengths expressed in terms of $x$. We need to find the value of $x$ using the given angle relationships. 2. **Focus on the intersecting lines figure (number 7):** It shows two lines intersecting, forming four angles. One angle is $60^\circ$ and the opposite angle is labeled $x$. 3. **Formula and rule:** Opposite (vertical) angles formed by two intersecting lines are equal. Therefore, $x = 60^\circ$. 4. **Conclusion:** The value of $x$ is $60$ degrees. This is the simplest and direct solution based on the given figures and angle relationships.