On any of the streets or portions of streets established by resolution of the council as angle-parking zones, when signs or pavement markings are in place indicating such angle parking, it is unlawful for the operator of any vehicle to park such vehicle except at the angle to the curb indicated by signs or pavement markings allotting space to parked vehicles, and entirely within the limits of such allotted space, with the front wheel nearest the curb within six inches of such curb. The provisions of this section shall not apply when such vehicle is actually engaged in the process of loading or unloading passengers, freight or goods, in which case such vehicle may be backed up to the curb, provided that such vehicle does not extend beyond the centerline of the street and does not block traffic thereby. (Ord. No. 938, § 1.)