1. **State the problem:** We need to find the value of $x$ that makes quadrilateral STUV a parallelogram. 2. **Recall the property of parallelograms:** Opposite sides of a parallelogram are equal in length. 3. **Set up the equation:** Since $UV$ and $TS$ are opposite sides, we have: $$x + 55 = 12x$$ 4. **Solve for $x$:** Subtract $x$ from both sides: $$\cancel{x} + 55 = 12\cancel{x}$$ $$55 = 11x$$ 5. **Divide both sides by 11:** $$\frac{55}{\cancel{11}} = \frac{11x}{\cancel{11}}$$ $$5 = x$$ 6. **Conclusion:** The value of $x$ that makes STUV a parallelogram is $x = 5$.