This is the 6659th most frequent Turkish word.
ağzı
The Turkish word "ağzı" means "mouth" (in the possessive form, e.g., "his/her/its mouth").
Here, 'ağzı' refers to the opening part of the book, metaphorically described as 'mouth'.
Kitabın ağzı açık bırakılmış.
The book's cover has been left open.
'Ağzına' refers directly to the physical mouth of the cat, showing possession by using -n suffix.
Kedinin ağzına süt koydum.
I put milk in the cat's mouth.
In this context, 'ağzından' refers to the spout of the teapot, which is compared to a mouth functionally.