KöMaL 2017 A695

We are given $2k$ lines, $e_1, \ldots, e_{2k}$ in a plane $S$, further given a line $g$ which has an angle $\alpha$ with $S$. Show that the sum of the pairwise angles between the lines $e_1, \ldots,e_{2k}, g$ is at most $(k^2+k)\cdot \dfrac \pi 2 + k\alpha.$