Hydrogen bonding in Cytosine and Guanine

[staralfur]

Homework Statement

The problem was to tell how many hydrogen bonds there are between cytosine and guanine. and I know there are three. http://study.com/cimages/multimages/16/Cytosine_Guanine_base_pair.png
But I think I might be misunderstanding the hydrogen bond concept.
I thought that hydrogen bonds only formed between O, F and N when they are also bond to H atom. And therefor CO₂ fx does not form hydrogen bond with water as the oxygen atoms in the CO₂ are not bonded to H atom.
In the cytosine-Guanine there is a hydrogen bond between Oxygen atom and NH₂ but the Oxygen atom is only bond to Carbon, so why is there a hydrogen bond?
And N makes hydrogen bond with NH but the N is only bond to two C atoms
please explain.

 

[Ygggdrasil]

Oxygen, fluorine or nitrogen atoms with available lone pairs can usually serve a hydrogen bond acceptor, and any hydrogen bonded to an F, O, or N can serve as a hydrogen bond donor. CO₂ lack hydrogens, so it cannot serve as a hydrogen bond donor. Although it has free lone pairs on its oxygens, CO₂ does not serve as a hydrogen bond acceptor because the molecule is not polar. The molecule is linear, so the dipoles from the two C=O bonds cancel each other out, and the molecule carries no net dipole (although, I'm not sure this explanation is entirely correct, because some sources I've found do suggest that carbon dioxide is capable of forming hydrogen bonds). Nevertheless, in guanine and cytosine, the oxygen atoms do carry a net dipole moment and can act as hydrogen bond acceptors.