http://www.issi1.com/corwin/calculator/table.txt


The is a protractor or Skill Tech ANGLE FINDER by
Hempe Manufacturing Co., Inc.
New Berlin, Wisconsin 53151
upc D9 M40760
It is a parallelogram that can reach to surfaces that don't meet
as well as inside and outside corners; ir reads the compliment as well
as +/- 45 deg;


There are tables at:
http://www.issi1.com/corwin/angles.txt
http://www.deltawoodworking.com/entry-4-projecthelp.html
http://www.scrollsaw.com/miter.html

However, non standard angles require a calculator:
http://www.issi1.com/corwin/calculator/crown.html
http://www.issi1.com/corwin/concurrentinverse.html

For your 45 deg inside and outside angles,
the tables agree:
                                        miter            bevel angle
                                        angle from top   undercut from front
                                                         angle from square

   32-58 molding 45 outside wall angel   75.6936          17.5512
                 45 inside wall angle   104.3064         -17.5512

The scrollsaw tables require interpolating for 52 between 50 and 55 deg
for the 8 sided example.  The deltawoodworking table gives 14.30 for
the compliment of 75.6936 for the 135 deg entry.

Still I do not know how the angles on your saw are defined so
it would be best to practice on some scraps to check that the signs
and compliments are correct.
                          
The coping saw method would work most of the time,
but it would be tedious for a lot of hardwood joints.
Also where a tight fit is needed for structural strength
it would not be good.  I started out calculating
concrete forms with a draft angle for internal voids.

It would be easiest to get a big enough saw so that the molding can be
fixtured at the 32-58 angle so that the saw could be set at the same
angle that is measured at the wall.  It also would not have to be a
compound saw.

The calculator menu is at http://www.issi1.com/corwin/concurrentinverse.html