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hardlikearmour is a trusted home cook.
The ounces are most likely weight, not volume. Per Rose Levy Beranbaum 1 egg white = 1.05 ounces= 2 T. So 15 ounces of egg whites translates to ~14 whites and equals 1 & 3/4 cups.
Sorry, hit reply too soon. I'd probably look at other angel food cake recipes to make sure the ratio of flour to whites is similar. In the Baking Bible by RLB the angel food recipe calls for 3.5 oz cake flour (1 cup if flour sifted into cup then leveled off) to 16 whites (2 cups/16.9 oz).
If I was going to punt, I'd split the difference and go with an extra white (1 & 7/8th cup) -- that way you're only off 2 T in either direction so reasonable chance it will work.
The angel food recipe in Bravetart has the same measurements (15oz or 2c). That book specifies that weight is the preferred measure in the intro, and volume measures like cups are rounded. So I'd go with the weight measure. But Stella Parks also says that unless a recipe specifies, either measure works. I'm not going to assume you're baking from Bravetart, but it sounds like you could use either measure and have a good cake.
June is a trusted source on General Cooking.
My mom's recipe called for 13 egg whites. I've never measured them otherwise, and it's always turned out.So I'm sorry I can't be of more help.