It seems that 3 angels were walking together; final destination, Sodom. Then, on the way they all stopped by and appeared to Abraham. Resuming the trip, what seemed to be the main angel, stayed back with Abraham to share with him what was about to happen in Sodom while the other 2 angels proceeded to the city. With that stay behind, a dialogue took place between Abraham and that angel when a kind of bargain developed which was used later in Judaism for the establishment of the Minyan which is the presence of 10 righteous to prevent a catastrophe. (Gen. 18:32) At this point, the dialogue ended and the presence of the angel was cut off while the presence of the 2 other angels was cut off when Lot and family had left the city.
It states;
The Lord appeared to Abraham near the great trees of Mamre while he was sitting at the entrance to his tent in the heat of the day. 2 Abraham looked up and saw three men standing nearby. When he saw them, he hurried from the entrance of his tent to meet them and bowed low to the ground.
3 He said, “If I have found favor in your eyes, my lord, do not pass your servant by. 4 Let a little water be brought, and then you may all wash your feet and rest under this tree. 5 Let me get you something to eat, so you can be refreshed and then go on your way—now that you have come to your servant.”
“Very well,” they answered, “do as you say.”
Not angels, God manifest as men.