1. **State the problem:** We are given two intersecting lines forming vertical angles. One angle measures 75° and the opposite vertical angle measures (5x)°. 2. **Formula and rule:** Vertical angles are always equal. So, we can set the two angles equal to each other: $$75 = 5x$$ 3. **Solve for x:** Divide both sides by 5: $$\cancel{5}x = \frac{75}{\cancel{5}}$$ which simplifies to: $$x = 15$$ 4. **Answer:** The value of $x$ is 15.