Angular displacement of a body is the angle in radians, degrees or revolutions through which a point or line has been rotated in a specified sense about a specified axis.
Angular displacement is traditionally assigned a positive sign when the sense of rotation is counter clockwise and negative, when the sense of rotation is clockwise.
In the given example, the point on the wheel is rotating 90 degrees from 12 o’clock to 3 o’clock. This makes the sense of rotation to be clockwise. Hence angular displacement should be –90ᵒ. Had the rotation been from 12 o’clock to 9 o’clock position, then the angular displacement would have been 90ᵒ.