The double and single angle thingy measure $x$ and $2x$ respectively. Case 1 - The known angle, $36^\circ$ is neither of these. This implies that $180 - 36 = 3x$, hence $x = 48$, $2x = 96$. So the angles in this case would be $(36, 48, 96)$. Case 2 - The known angle, $36^\circ$ measures $2x$, this implies that $x = 18$, so the other angle would be $126$, hence our angles in this case would be $(18, 36, 126)$. Case 3 - The case we throw in the trash - The known angle, $36^\circ$ measures $x$, this would imply that $2x = 72^\circ$, and the other angle would be $72^\circ$, but this would imply this is an isosceles triangle, so we throw this case in the trash.

You don't see parmenides51 posting many problems in MSM. @above does a nice job with casework.