The mode of angelic knowledge is not discursive (reasoning from one premises to conclusions, as in human knowledge) but intuitive.
Addressing whether an angel knows God by his own natural principles, St. Thomas Aquinas answers (Summa Theologica I q. 56 a. 3 c.):
The angels can have some knowledge of God by their own principles. In evidence whereof it must be borne in mind that a thing is known in three ways: first, by the presence of its essence in the knower, as light can be seen in the eye; and so we have said that an angel knows himself—secondly, by the presence of its similitude in the power which knows it, as a stone is seen by the eye from its image being in the eye—thirdly, when the image of the object known is not drawn directly from the object itself, but from something else in which it is made to appear, as when we behold a man in a mirror.
To the first-named class that knowledge of God is likened by which He is seen through His essence; and knowledge such as this cannot accrue to any creature from its natural principles, as was said above (q. 12, a. 4). The third class comprises the knowledge whereby we know God while we are on earth, by His likeness reflected in creatures, according to Rm. 1:20: "The invisible things of God are clearly seen, being understood by the things that are made." Hence, too, we are said to see God in a mirror. But the knowledge, whereby according to his natural principles the angel knows God, stands midway between these two; and is likened to that knowledge whereby a thing is seen through the species abstracted from it. For since God's image is impressed on the very nature of the angel in his essence, the angel knows God in as much as he is the image of God. Yet he does not behold God's essence; because no created likeness is sufficient to represent the Divine essence. Such knowledge then approaches rather to the specular kind; because the angelic nature is itself a kind of mirror representing the Divine image.
Regarding "inter-angelic" communication (angels communicating to each other), see: The Thomist 68 (2004): 205-58 on the semiosis (action of signs) of angels.