How to draw a solid with multiple radius filets?

Draw the top profile, and extrude with 5° of draft.
Add the hinge looking extrusion.
Remove material from the side view to match the profile
Apply a few fillets
Shell to the required material thickness

The model looks interesting, I may make it later if I can get my head around these "backwards" views :)

You are doing this in CATIA Part Design (solids)?

For the multifple corners around the top; use a Variable Fillet Radius command, and click on the vertices where the radius changes from R5 to R10.

Here is how I would go about modeling it...

In SW2017 I used a variable fillet and selected the R20 edge between the two different radi.

I have included a SW2017 native part file and a STEP file to show how I went about modeling this part.

Here is my own model. It differs a bit from what Stephen uploaded.
Some of those dimensions were a little unclear, so multiple interpretations are the result.
The final image helps to see some of the differences between the two models. One in green, the other in yellow to celebrate the nice missing colors from SOLIDWORKS' past.