8. Use lines parallel to the sides of an equilateral triangle to divide it into \( n^{2} \) smaller equilateral triangles, each with a side length of 1.
8. The total number of vertices of the small triangles on the left is
$$
1+2+\cdots+(n+1)=\frac{1}{2}(n+1)(n+2) \text {, }
$$

This means that the broken line consists of $\frac{1}{2}\left(n^{2}+3 n\right)$ small line segments. If we color all the small triangles that are similar to the original triangle and have the same orientation black (see the right figure), then there are at least $n$ black triangles, each containing two adjacent line segments of the broken line, with the angle between them being $60^{\circ}$.