1. Let us denote by $\lambda$ (where $\lambda >1$) the ratio of the sides of a parallelogram. Find, in terms of $\lambda$, the maximum possible measure of the acute angle formed by the diagonals. 2. Consider the diagonals of a convex $n$-gon. Upon omitting any $n-3$ of them, prove that among the remaining diagonals there are $n-3$ ones that do not intersect inside the polygon. On the other hand, show that one can always omit $n-2$ diagonals so that the previous assertion is not true anymore. 3. We are given the sets $H_1\mathrm{,}{H}_2\mathrm{,}\text{...}\mathrm{,}{H}_n$. The set $H_k$ ($k=\mathrm{1,2,}\text{...}\mathrm{,}n$) consists of $k$ pairwise disjoint intervals of the real line. Prove that among the intervals that form the sets $H_k$ one can find $\left[\left(n+1\right)/2\right]$ pairwise disjoint ones, each of which belongs to a different set $H_k$. ($\left[x\right]$ denotes the largest integer that is less than or equal to $x$.)