489. The more sides a regular polygon has, the more convex its periphery becomes; to what limit does the internal (external) angle tend when the number of sides increases indefinitely?
489. The angle of a regular $n$-sided polygon $\frac{180^{\circ}(n-2)}{n}=180^{\circ}$ $\left(1-\frac{2}{n}\right)$ approaches $180^{\circ}$ as $n \rightarrow \infty$. The polygon approaches the shape of a circle, and the angle (interior) between two consecutive sides approaches the angle (at $180^{\circ}$) formed by two halves of the tangent to the circle.