1. **State the problem:** We are given two vertical angles formed by intersecting lines. One angle measures 130° and the other measures (3x - 20)°. We need to write an equation to find the value of $x$. 2. **Recall the rule:** Vertical angles are congruent, meaning they have equal measures. 3. **Set up the equation:** Since the angles are vertical angles, we have: $$130 = 3x - 20$$ 4. **Solve the equation:** Add 20 to both sides: $$130 + 20 = 3x - 20 + 20$$ $$150 = 3x$$ Divide both sides by 3: $$\frac{150}{\cancel{3}} = \frac{3x}{\cancel{3}}$$ $$50 = x$$ 5. **Final answer:** $$x = 50$$ This equation and solution allow us to find the value of $x$ based on the given angle measures.