Acrylic, which I think is more formally known as polymethylmethacrylate, is an old traditional material for aircraft canopies and for transparent tools like navigation slide rules and such. It has a characteristic odor that appears when it is drilled or sawed. ... okay, all plastics have their own odor. I think PMMA is continuous cast from solvent solution, on a large chrome plated wheel. ... or once was; there are probably other ways to get it into useful form now.
I have a protractor almost exactly like the one in the photo. Mine is at least 55 years old. The blue cast suggests polycarbonate, which is often blued slightly to offset a normal yellow cast, but I don't think PC was common that long ago, so I'm guessing a polystyrene alloy.
Polystyrene is cheap, clear and colorless, but brittle. You may remember it from the transparencies in plastic model kits. Nowadays, except for plastic models, you'll probably find styrene alloyed with acrylonitrile (vinyl cyanide) as SAN, or acrylonitrile and butadiene as ABS, or a thousand other things sold under a million names. ... well, almost.
Polysulfone is a little more yellow than polycarbonate, less subject to environmental stress cracking, more temperature resistant, similarly tough and similarly priced.
You might want to visit your local plastic sheet seller to buy a few sheets of various thicknesses and compositions, to get a feel for how stiff you want your product and how difficult it will be to fabricate it from sheet.
I'm guessing your protractor was screen printed (in two steps, one for each color), which requires some care to get good registration. Your screen printer may not like it, but you can specify epoxy ink for durability. Start with whatever ink the printer suggests, and test a few samples yourself.
Mike Halloran
Pembroke Pines, FL, USA