This hexagonal roof has hip rafters that are both a hip and a valley rafter at the same time. It also would have one roof slope angle that can only be calculated from the geometry of the roof. In my example I've used an 5:12 pitch as the main roof pitch with the adjacent hexagonal eave angle having an 12:12 roof pitch.
If the World Skills International Competition judges are expecting perfect cuts from the competitors, then maybe they could use my Rafter Tools apps to check the accuracy of the competitors geometry. I tested my new and improved plan angle formula on this hexagonal roof and it returned the correct plan angles for the 3 different roof pitch angles with the 3 different eave angles.
Just found these drawing for the World Skills International Competition in 2010 & 2011. The drawing is showing a roof with the purlin rafter projecting under the hip rafter. The student would have to know how to geometrically draw out the purlin lip cut angle. The World Skills International Competition allows carpenters to use calculators. Maybe the World Skills International Competitors could use the Rafter Tools calculator?
Here are a couple of drawings showing how to draw out the purlin lip cut angle.