how did Lord of the Eagles and the great birds save Gandalf, the dwarves and Bilbo from the wolves and Goblins

Gandalf knows that he must do something and so he starts a fire in the midst of the wolves, attracting the attention of the Lord of the Eagles. Goblins arrive on the scene to mock the pained wolves and in a clever move, they burn fires around the trees in order to trap the dwarves. The Lord of the Eagles arrives and carries Gandalf away, just in time, and other birds come and save the dwarves and Bilbo. And so, the chapter ends with Bilbo lodged in a safe place, sleeping soundly.