Sum of Angles between Straight Lines at Point form Four Right Angles

Corollary to Two Angles on Straight Line make Two Right Angles
If any number of straight lines are drawn from a given point, the sum of the consecutive angles so formed is $4$ right angles.

Proof
Let $OA_1, OA_2, \ldots, OA_n$ be straight lines drawn from a point $O$ to points $A_1, A_2, \ldots, A_n$.

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 $OA_j$.