1. **State the problem:** We have a quadrilateral with two sides measuring 11 cm and 15 cm, and the angle between them is 120°. We want to find the length of side $c$ opposite the 120° angle. 2. **Identify the formula:** To find side $c$ opposite an angle in a triangle, we use the Law of Cosines: $$c^2 = a^2 + b^2 - 2ab \cos(\theta)$$ where $a=11$, $b=15$, and $\theta=120^\circ$. 3. **Calculate $c^2$:** $$c^2 = 11^2 + 15^2 - 2 \times 11 \times 15 \times \cos(120^\circ)$$ Calculate each term: $$11^2 = 121$$ $$15^2 = 225$$ $$\cos(120^\circ) = -0.5$$ Substitute: $$c^2 = 121 + 225 - 2 \times 11 \times 15 \times (-0.5)$$ $$c^2 = 346 + 165 = 511$$ 4. **Find $c$ by taking the square root:** $$c = \sqrt{511} \approx 22.6$$ 5. **Conclusion:** The length of side $c$ opposite the 120° angle is approximately 22.6 cm.