1. **State the problem:** We need to find the number of sides of a polygon whose sum of interior angles is 3600°. 2. **Formula:** The sum of interior angles $S$ of a polygon with $n$ sides is given by: $$S = 180(n - 2)$$ 3. **Apply the formula:** Substitute $S = 3600$: $$3600 = 180(n - 2)$$ 4. **Solve for $n$:** Divide both sides by 180: $$\cancel{180}(n - 2) = \cancel{180} \times 20$$ $$n - 2 = 20$$ Add 2 to both sides: $$n = 20 + 2$$ $$n = 22$$ 5. **Answer:** The polygon has **22 sides**.