1. **State the problem:** We need to find the number of sides $n$ of a regular polygon given that each interior angle measures 140°. 2. **Formula for interior angle of a regular polygon:** $$\text{Interior angle} = \frac{(n-2) \times 180}{n}$$ where $n$ is the number of sides. 3. **Set up the equation:** Given interior angle = 140°, so $$140 = \frac{(n-2) \times 180}{n}$$ 4. **Solve for $n$:** Multiply both sides by $n$: $$140n = (n-2) \times 180$$ 5. **Expand the right side:** $$140n = 180n - 360$$ 6. **Bring all terms involving $n$ to one side:** $$140n - 180n = -360$$ 7. **Simplify:** $$-40n = -360$$ 8. **Divide both sides by -40:** $$n = \frac{-360}{-40}$$ $$n = 9$$ 9. **Answer:** The polygon has 9 sides.