Jack Purlin intersects Hip or Valley Rafter
Study of Shelf Cut following the line parallel to the long axis of the Hip or Valley Rafter

P2 ... Jack Rafter Side Cut Angle. Saw Miter Angle on the shoulder of the jack purlin set in the surface of the roof, at the intersection of the purlin and the Valley rafter. C5 ... Backing Angle. Saw Blade Bevel Angle to make the cut along the miter line created by angle 90° – P2. P3 ... Angle produced by plane of the shelf cut intersecting the face of the jack purlin set perpendicular to the surface of the roof. Backing Angle C5 as viewed when projected to the face of the jack purlin set perpendicular to the surface of the roof, or C5 rotated through angle P2. R3 ... Angle traced on the unbacked shoulder of a Valley rafter, where the Valley intersects the face of the purlin set perpendicular to the surface of the roof. Also the miter angle on the unbacked upper shoulder of the Hip rafter to accommodate square fascia; 90° – R3 is the Square Fascia Side Cut Angle. C2 ... 90° ± C2 is the dihedral angle measured between the face of the purlin set perpendicular to the surface of the roof and the lower (unbacked) shoulder of a Valley rafter. Also the Saw Blade Bevel to cut the Hip or Valley rafter from its unbacked shoulder, along the miter line produced by angle 90° – R3, to accommodate Square Fascia.