1. **State the problem:** We have two intersecting lines at point E, creating angles (5x)° and 65° that are opposite each other. 2. **Identify the relationship:** Vertical angles formed by intersecting lines are equal. Therefore, the angle (5x)° equals 65°. 3. **Write the equation:** $$5x = 65$$ 4. **Solve for x:** Divide both sides by 5: $$\cancel{5}x = \cancel{5} \times 13$$ $$x = 13$$ 5. **Answer:** $$x = 13$$ This means the value of x that satisfies the angle relationship is 13.