1. **State the problem:** Find the perimeter of sector AOB of a circle with radius 18 cm and central angle 80°. 2. **Recall the formula for arc length:** $$\text{arc length} = \frac{\theta}{360} \times 2\pi r$$ where $\theta$ is the central angle in degrees and $r$ is the radius. 3. **Calculate the arc length:** $$\frac{80}{360} \times 2\pi \times 18 = \frac{80}{360} \times 36\pi = \frac{80 \times 36\pi}{360}$$ Simplify the fraction: $$\frac{80 \times 36\pi}{360} = \frac{\cancel{80}^{{\times 1}} \times 36\pi}{\cancel{360}^{{\times 4.5}}} = \frac{8\pi}{1} = 8\pi$$ 4. **Find the perimeter of the sector:** The perimeter is the sum of the two radii and the arc length: $$18 + 18 + 8\pi = 36 + 8\pi$$ 5. **Final answer:** The perimeter of sector AOB is $$36 + 8\pi$$ cm.