In this clever video by Toolrank you can see a recip blade used to draw circles, produce square layout, and bisect angles. Drawing circles is not that exciting but about half-way through, the guy in the video begins to lay out and bisect angles. Near the end he bisects a 90 to get a 45, but he could just as easily have bisected an angle that was not a perfect 90. In the days before accurate digital protractors this is how carpenters figured out the miter cuts for crown and running trim in rooms that were not quite square. That's how I used to do it, though I used a compass because it wouldn't have occurred to me to use a recip saw blade.
For more on unusual layout methods involving a compass and a tool known as a joggle stick see Scribing for a Perfect Fit.