1. **State the problem:** Each interior angle of a regular polygon measures 160°. We need to find the number of sides of this polygon. 2. **Recall the formula for the interior angles of a regular polygon:** The measure of each interior angle $I$ of a regular polygon with $n$ sides is given by: $$I = \frac{(n-2) \times 180}{n}$$ 3. **Substitute the known value:** Here, $I = 160$, so: $$160 = \frac{(n-2) \times 180}{n}$$ 4. **Multiply both sides by $n$ to eliminate the denominator:** $$160n = 180(n - 2)$$ 5. **Expand the right side:** $$160n = 180n - 360$$ 6. **Bring all terms involving $n$ to one side:** $$160n - 180n = -360$$ $$-20n = -360$$ 7. **Divide both sides by -20:** $$n = \frac{-360}{-20} = 18$$ 8. **Conclusion:** The polygon has $18$ sides.