In trigonometry an angle is usually drawn in what is called the "standard position" as shown above. In this position, the vertex (B) of the angle is on the origin, with a fixed side lying at 3 o'clock along the positive x axis.
The other side, called the 'terminal side' is the one that can be anywhere and defines the angle. In the figure below, drag point A and see how the position of the terminal side BA defines the angle.
See also Angle definition and properties - Trigonometry