58. (8th grade) Given a thousand-sided polygon. Inside it, 500 points are taken, which are connected to each other and to the vertices of the thousand-sided polygon. How many triangles will be formed? (The sides of the triangles do not intersect).
58. Let $x$ be the number of triangles, $2 d(n-2)$ be the sum of the interior angles of a polygon, $2 d x$ be the sum of the interior angles of the triangles, and $4 d \cdot 500$ be the sum of the full angles at the given 500 points. We can set up the equation $2 d x = 500 \cdot 4 d + 2 d(n-2)$, where $n=1000$. Answer: $x=1998$.