We have been asked to find
In which quadrant does the terminal side of the angle 257° lie?
As we know that in the first Quadrant angle is from 0 to 90
In the second Quadrant angle is from 90 to 180
In the third Quadrant angle is from 180 to 270.
In the fourth Quadrant angle is from 270 to 360.
Hence the angle 257 will lie in the third Quadrant.