1. **State the problem:** We are given a regular convex polygon where each interior angle measures 144°. We need to find how many sides the polygon has. 2. **Formula for interior angle 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 given interior angle:** We know $I = 144$, so: $$144 = \frac{(n-2) \times 180}{n}$$ 4. **Solve for $n$:** Multiply both sides by $n$: $$144n = 180(n-2)$$ 5. **Expand the right side:** $$144n = 180n - 360$$ 6. **Bring all terms to one side:** $$144n - 180n = -360$$ 7. **Simplify:** $$\cancel{144}n - \cancel{180}n = -360$$ $$-36n = -360$$ 8. **Divide both sides by -36:** $$\frac{-36n}{\cancel{-36}} = \frac{-360}{\cancel{-36}}$$ $$n = 10$$ 9. **Interpretation:** The polygon has 10 sides. **Final answer:** The polygon has $\boxed{10}$ sides.