1. **State the problem:** We need to find the measure of angle $x$ in a triangle with sides 40 cm, 18 cm, and 25 cm, where $x$ is the angle between the 40 cm and 25 cm sides. 2. **Formula used:** Use the Law of Cosines, which relates the sides and angles of a triangle: $$\cos(x) = \frac{a^2 + b^2 - c^2}{2ab}$$ where $a$ and $b$ are the sides enclosing angle $x$, and $c$ is the side opposite angle $x$. 3. **Identify sides:** Here, $a = 40$, $b = 25$, and $c = 18$ (opposite angle $x$). 4. **Apply the Law of Cosines:** $$\cos(x) = \frac{40^2 + 25^2 - 18^2}{2 \times 40 \times 25}$$ Calculate squares: $$\cos(x) = \frac{1600 + 625 - 324}{2000}$$ Simplify numerator: $$\cos(x) = \frac{1901}{2000}$$ 5. **Calculate cosine value:** $$\cos(x) = 0.9505$$ 6. **Find angle $x$:** $$x = \cos^{-1}(0.9505)$$ Using a calculator: $$x \approx 18.1^\circ$$ 7. **Final answer:** The measure of angle $x$ is approximately **18.1 degrees**.