well, she knows that the mass of chocolate is 1.8 times that of powered sugar.
it just so happen that powered sugar is 100 grams for one cup, and since chocolate is 1.8 times "that", then in one cup of chocolate there must be 1.8 times 100 grams, or 1.8*100 = 180 grams.
the recipe uses 1/2 cup of chocolate, well, half a cup of chocolate, namely half of 180 grams is just 90 grams.