Sum of Angles between Straight Lines at Point form Four Right Angles
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Corollary to Two Angles on Straight Line make Two Right Angles
Let $OA_1$ be produced past $O$ to $B$.
Then $OB$ either coincides with $OA_j$ for some $j$ between $1$ and $n$, or $OB$ divides angle $A_j O A_k$ for some $j, k$ between $1$ and $n$.
First suppose $OB$ coincides with $OA_j$.
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