deletions | additions       diff --git a/Observe_the_angles_angle_PQ__.tex b/Observe_the_angles_angle_PQ__.tex  index 668a885..dac2173 100644  --- a/Observe_the_angles_angle_PQ__.tex  +++ b/Observe_the_angles_angle_PQ__.tex 
...
In this case, $Q=Q'$.  Observe the angles $\angle PQ'A$ and $\angle PQ'B$. WLOG assume $\angle PQ'B$ is the larger of the two and denote it $\alpha$. \begin{align*}  \angle PQ'A + \angle PQ'B &= \pi \\