1. **State the problem:** We are given two parallel lines cut by a transversal, creating angles $ (6x + 12)^\circ $ and $ 132^\circ $. We need to solve for $ x $. 2. **Identify the relationship:** Since the lines are parallel and the angles are on the same side of the transversal but on different lines, these angles are corresponding or alternate interior angles, which are equal. 3. **Set up the equation:** $$6x + 12 = 132$$ 4. **Solve for $ x $:** Subtract 12 from both sides: $$6x = 132 - 12$$ $$6x = 120$$ Divide both sides by 6: $$x = \frac{120}{6}$$ $$x = 20$$ 5. **Conclusion:** The value of $ x $ that satisfies the angle relationship is $ 20 $.