1. **State the problem:** We are given a sector OAB of a circle with radius $r = 4.6$ mm and sector area $A = 18$ mm². We need to find the central angle $\theta$ in degrees to 1 decimal place. 2. **Formula for the area of a sector:** The area $A$ of a sector with radius $r$ and central angle $\theta$ (in degrees) is given by: $$A = \frac{\theta}{360} \times \pi r^2$$ 3. **Rearrange the formula to solve for $\theta$:** $$\theta = \frac{360 \times A}{\pi r^2}$$ 4. **Substitute the known values:** $$\theta = \frac{360 \times 18}{\pi \times (4.6)^2}$$ 5. **Calculate the denominator:** $$4.6^2 = 21.16$$ 6. **Calculate the fraction:** $$\theta = \frac{360 \times 18}{\pi \times 21.16}$$ 7. **Calculate numerator and denominator separately:** $$360 \times 18 = 6480$$ 8. **Calculate $\pi \times 21.16$:** $$\pi \times 21.16 \approx 3.1416 \times 21.16 = 66.47$$ 9. **Calculate $\theta$:** $$\theta = \frac{6480}{66.47} \approx 97.5$$ 10. **Final answer:** The central angle $\theta$ is approximately **97.5 degrees** to 1 decimal place.