1. **State the problem:** We need to find the measure of angle $C$ in a triangle where sides $a=18$, $b=22$, and $c=20$ are given. 2. **Formula used:** The Law of Cosines states: $$c^2 = a^2 + b^2 - 2ab \cdot \cos(C)$$ This formula relates the lengths of the sides of a triangle to the cosine of one of its angles. 3. **Rearrange the formula to solve for $\cos(C)$:** $$\cos(C) = \frac{a^2 + b^2 - c^2}{2ab}$$ 4. **Substitute the known values:** $$\cos(C) = \frac{18^2 + 22^2 - 20^2}{2 \times 18 \times 22} = \frac{324 + 484 - 400}{792} = \frac{408}{792}$$ 5. **Simplify the fraction:** $$\cos(C) = 0.5151515...$$ 6. **Find angle $C$ by taking the inverse cosine:** $$C = \cos^{-1}(0.5151515)$$ Using a calculator, $$C \approx 58.94^\circ$$ 7. **Final answer:** The measure of angle $C$ is approximately **58.94 degrees** rounded to the nearest hundredth.