The two latches make known the fact that this is an isosceles triangle. Here, x is the base angle. There are two base angles in isosceles triangles. Base angles have the same measure. This explains the reason for 2x in the equation below.
The number of shelves must be a factor of the number of books from each category. (Because you are using multiple shelves). You are looking for the greatest amount, so you need to greatest, common factor (GCF) from each bunch of books.