backing cut

Backing Angle ... the animated version. The right angle at the corner can actually be any value.
Construction of the Backing Angle
Backing Angle: Regular Octogonal Gazebo

Setting the length of the Hip run equal to one, the length of the line perpendicular to the Hip rafter and forming the rise of the backing angle is sin Hip Pitch Angle. The line of the backing angle run in plan view equals tan Plan Angle.

Since the rise/run of an angle is the tangent we can derive the well known formula (one of many ...) for the backing bevel:

tan Backing Angle = sin Hip Pitch Angle ÷ tan Plan Angle

Taking the arctangent of both sides of the equation:
Backing Angle = arctan (sin Hip Pitch Angle ÷ tan Plan Angle)

Options!

I like representing the angles on paper and then using a bevel. For instance once I have the offset and the rise of the backing angles, you can lay out your hip with the offset on the top (unbacked) and then layout the two faces (should be the same measurement from the top of the unbacked hip). Place your bevel on your drawing along the hip centerline and a corresponding backing angle and then use this angle to set your saw.

by the way does anyone cut their plumb cuts at the top of the hip after the backing cut? It sure is hard when you have to start at the top of the hip with the backing cut after the plumb cuts have been made.

If you are using a chain saw there isn't really any preferred order to cutting. We generally mark all the lines on the squared off end: side cuts, plumb cuts, chamfers for the housing. The backing planes may be cut before or after the plumb/side cuts on the end of the rafter.

If the plumb/sides cuts have been made you can make the cut along the plumb plane created at the Valley peak by marking the miter line (R5 in Hawkindale angles) and setting the saw blade bevel to the common rafter pitch angle.