1. **State the problem:** We have a sector OAB of a circle with radius $r = 4.3$ mm and area $14$ mm². We need to find the central angle $\theta$ in degrees to 1 decimal place. 2. **Formula for the area of a sector:** $$\text{Area} = \frac{\theta}{360} \times \pi r^2$$ where $\theta$ is in degrees. 3. **Substitute known values:** $$14 = \frac{\theta}{360} \times \pi \times (4.3)^2$$ 4. **Calculate $r^2$:** $$4.3^2 = 18.49$$ 5. **Rewrite the equation:** $$14 = \frac{\theta}{360} \times \pi \times 18.49$$ 6. **Isolate $\theta$:** $$14 = \frac{\theta \pi 18.49}{360}$$ Multiply both sides by 360: $$14 \times 360 = \theta \pi 18.49$$ 7. **Simplify left side:** $$5040 = \theta \pi 18.49$$ 8. **Divide both sides by $\pi 18.49$:** $$\theta = \frac{5040}{\pi \times 18.49}$$ Show cancellation: $$\theta = \frac{5040}{\cancel{\pi} \times 18.49} \times \frac{1}{\cancel{\pi}}$$ 9. **Calculate denominator:** $$\pi \times 18.49 \approx 3.1416 \times 18.49 = 58.08$$ 10. **Calculate $\theta$:** $$\theta = \frac{5040}{58.08} \approx 86.7$$ **Final answer:** $$\boxed{\theta \approx 86.7^\circ}$$