KöMaL problem A, 2017

Geometry Difficulty 6.0 National Olympiad Prove it Hungary

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

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