Place a ladder near the angles you will need to measure. Ensure the ladder will allow you to reach the angles for measuring safely.
Place one side of the adjustable protractor against one wall in the angle. Move the other side of the protractor to the other wall. Note the angle for that specific corner of the ceiling.
Lay the crown molding on a flat surface, such as a portable workbench or sawhorses.
Transfer the angle measurements to the crown molding using the protractor and a pencil.
Use a wood saw to cut the crown molding along the line you drew to match the angle. Use sandpaper to smooth the rough cut area of the molding.
Repeat the process to measure angles and cut the remaining pieces of crown molding for the cathedral ceiling.