1. **State the problem:** We need to find the number of sides $n$ of a regular polygon given that each interior angle measures 172°. 2. **Formula for interior angle of a regular polygon:** $$\text{Interior angle} = \frac{(n-2) \times 180}{n}$$ 3. **Set up the equation:** $$172 = \frac{(n-2) \times 180}{n}$$ 4. **Multiply both sides by $n$ to clear the denominator:** $$172n = 180(n-2)$$ 5. **Distribute 180 on the right side:** $$172n = 180n - 360$$ 6. **Bring all terms involving $n$ to one side:** $$172n - 180n = -360$$ 7. **Simplify the left side:** $$\cancel{172}n - \cancel{180}n = -360$$ $$-8n = -360$$ 8. **Divide both sides by -8:** $$\frac{-8n}{\cancel{-8}} = \frac{-360}{\cancel{-8}}$$ $$n = 45$$ **Final answer:** The polygon has **45 sides**.