Final answer:
The angle of a displacement vector counterclockwise from the x-axis is determined by its components. Negative x-components suggest the vector points left, with positive angles being counterclockwise from the positive x-axis. The exact angle can be measured using vector component direction and magnitude.
Step-by-step explanation:
The angle of a displacement vector as measured counterclockwise from the x-axis can be understood by examining both the direction of the vector components and the conventions used for measuring angles in vector operations. When handling vector components, the x-component will determine the horizontal direction, while the y-component determines the vertical direction. If the x-component is negative, then the vector points to the left which is the negative direction of the x-axis.
Furthermore, angles are positive when measured in a counterclockwise direction from the positive x-axis and negative when measured clockwise. For example, if on the third leg of a journey a displacement vector has a magnitude of 50.0 m and is directed 30° west of north, its counterclockwise angle from the positive x-axis (east direction) is calculated as 120°.
If a displacement vector has an x-component Δx = -4.0, this indicates that the displacement is in the opposite direction to the positive x-axis, implying that the angle is between 90° and 270° since it is directed to the left (west when considering standard directional conventions).