Abstract: Conway, Croft and Erd\H{o}s (1979) investigated the following problem: Let $n$ points in the plane given, no three on a line. They form exactly $N=\frac{1}{2}n(n-1)(n-2)$ angles. Let $0< \alpha< \pi$ and denote by $f(n, \alpha)$ the greatest integer such that there are at least $f(n,\alpha)$ angles exceeding $\alpha$ for every choice of $n$ such points. They showed that $F(\alpha)=\lim _{n\to \infty} f(n,\alpha)/N$ exists and is decreasing. Obviously, $F(\alpha)=1/3$ for all $0< \alpha \leq \pi/3$, because at least one third of the angles exceed $\pi/3$. They conjecture, e.g., that the maximum number of acute angled triangles is $(1+o(1))\frac{5}{9}{n \choose 3}$.
In this talk we determine further values of $F$ and consider other related problems. We also point out connections to Turan type extremal hypergraph problems.