Miguel received a $50 gift card to the bookstore. he would like to buy 3 books that cost$ 15.75 each including tax. he estmates that he cannot bey all three book because each book cost about $20, and all three book would cost $60 .is his estimate resonable? explain your reasoning.

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.