Coterminal angles are angles in coordinate plane that result out of rotation of the terminal side of angles in standard position. The angle in standard position has the vertex at the origin and one ray on the positive x -axis, which is called the initial side of the angle. The other ray is called the terminal side of the angle.
Coterminal Angles
In the above example angle measure 45º has initial side on the x-axis and the terminal side along OP. If you imagine OP to be a circling ray, it comes back to the same position after completing one full rotation about the origin. Thus it has described an angle measure of 405º. Angles 45 and 405º both share the terminal ray along OP. If the rotation of OP is continued, it describes angles 765º, 1125º ..... after completing each rotation. All these angle measures are Coterminal angles.
The Coterminal angles makes it possible for the angle to have any real number as its measure and map all these measures to Unit circle angles.

Two angles in standard position are called coterminal angles if they have the same terminal side.
As coterminal angles result due to the rotation of the terminal side, they differ in multiples of 360º.
Coterminal angle to a given angle can be found by adding or subtracting multiples of 360 to the given angle.

An angle measure is positive if the rotation from the initial side to the terminal side is counter clockwise and negative if the rotation is clockwise. It is also possible for a positive angle and a negative angles to be coterminal angles.

Coterminal Definition

The Quadrant angle 270º is formed by the counter clockwise rotation of the terminal side OP. When the terminal side is rotated in the clockwise direction, it coincides with OP when it describes 90º.
Thus the angles 270 and -90 are coterminal angles.
Thus Coterminal angles can also be defined as,
If θ is the measure of an angle then all angles with a measure of θ + 360n where n is an integer are Coterminal with θ.