How do I figure out this angle?

Micheal, I think I understand what you're saying but I don't believe your method accounts for the 10 degree slope on the front pieces. 

As for cutting the stock, I'd cut it as if it were crown, nested.

All of this has peaked my curiosity. I'm going to have to make some time to play with this, I've gotta know the answer now.
 
One challenge will be that the front molding will need to be 'deeper' to account for the 10 degree slope to match up properly with the sides. 

One of two things will happen on the column, it's a matter of making a decision of what look you are after.

A;  the top of the molding profile projection will be narrower than the sides and be difficult to hide on the miter.  If a releif cut was made to be perpendicular to the sides, then the typical 45-45 =90 miter would work and the relief cut would hide any discrpency of the miter and molding being shy on the front-top.  The molding could be cut, glued, and placed on the column all in one step.    This treatment probably wouldn't look noticeable to the viewer since you won't be looking down on it, and you will see the underside more often.

B:  If you want to  have the same profile projection on the top of the molding aroung the column, the bottom of the molding must be 'made up' to allow for the slope of the column.  If you would cut your unaltered moldings at a typical 45 degree miter, then add on a 10 degree backer to the front piece, or put it on the column as a nailer, this should work.  This will look 'heavier' from the seated position.

I don't think a compound miter will work in this situation with the applied trim.  Crown yes, trim no.

 
Brice Burrell said:
Micheal, I think I understand what you're saying but I don't believe your method accounts for the 10 degree slope on the front pieces

As for cutting the stock, I'd cut it as if it were crown, nested.

All of this has peaked my curiosity. I'm going to have to make some time to play with this, I've gotta know the answer now.

It does... but CD said it more succinctly in his reply.

Also, I only addressed the small molding that is fully nailed to the sides of the column.
I think dealing with the crown is easier since only the lower portion of the crown contacts
the variable sloping column, and I'd cut it upside down as usual.

In the case of the crown it might be worthwhile to shim (make a spacer) the top of the
crown out from the fence the equivalent of 10 degrees instead of back beveling the lower
portion of the crown. If that is done the pieces on the sides of the columns will only have
a scant tangential contact with the column so a filler block should be added for strength.

 
Did you want the front piece of trim to be tilted down @ 10&deg as well?  If not, it would be a simple 45&deg cut (with a wedge shaped backer piece for the front trim).  If the front trim -is- tilted down then you'd need to cut a 10&deg angle out of the back of the side piece of trim to tilt the side trim downward (otherwise the corner details would not line up).  Think of a more extreme (angle) case with 2 rectangles (instead of complex moulding curve) to see how these 2 pieces must be at the same angle for them to match up.  Once both pieces are 'tilted' at the same angles then you'll use the previously posted miter calculator.

Alternatively, butt the pieces together and round off the corner for a rounded transition (instead of the pointed corner).
 
Sorry, I forgot to post pics of the finished project.  The molding turned out fine.  There are gaps at the top of the joint if you're looking down from the top of the frame.  Luckily no one will ever have that perspective.
 
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