1. Preheat the oven to 350°F.
2. Sift the flour twice with the cocoa powder and 1/2 cup of the sugar.
3. With an electric mixer on high speed, beat the egg whites, cream of tartar and salt until soft peaks form when the mixer is removed from the batter.
4. Add half of the remaining sugar and beat for 1 minute. Add the remaining sugar, 2 tablespoons at a time, beating after each addition.
5. Stir in the vanilla.
6. Fold the flour and sugar mixture into the egg whites, 1/4 cup at a time, until just incorporated.
7. Put the batter in an ungreased 10" tube pan and bake until the cake is light golden brown and springy to the touch, about 1 hour. Invert the pan and let the cake cool completely before removing from the pan.
8. Place 1 slice of Chocolate Angel Cake on each of 6 plates. Spoon Chocolate Sauce on the side of the cake. Arrange the orange segments like a fan to the side of the sauce.