Question 72
$n \gt 10$ is a positive integer. $n$ lines are drawn on the plane such that no three are concurrent and no two are parallel. Among the finite regions formed by these lines, at least $\frac{n^2}{8} + 1$ of them were blacked. We call a triangle formed by three lines *good* if there is only one black region inside of it. Prove that we at least have $\frac{n}{2}$ good triangles.
*Note. We call a region finite if its area is finite.*
*Note. We call a region finite if its area is finite.*