1. **State the problem:** We have two intersecting lines forming two angles: one is 130° and the other is (3x - 20)°. We need to write an equation to find the value of $x$. 2. **Important rule:** When two lines intersect, opposite (vertical) angles are equal. 3. **Apply the rule:** Since the angles 130° and (3x - 20)° are vertical angles, they are equal. 4. **Write the equation:** $$130 = 3x - 20$$ 5. **Solve for $x$:** Add 20 to both sides: $$130 + 20 = 3x - 20 + 20$$ $$150 = 3x$$ Divide both sides by 3: $$\frac{150}{\cancel{3}} = \frac{3x}{\cancel{3}}$$ $$50 = x$$ 6. **Final answer:** $$x = 50$$