No vehicle shall be parked with the left side of such vehicle next to the curb, except on one-way streets, and it shall be unlawful to stand or park any vehicle in a street other than parallel with the curb and with the two (2) right wheels of the vehicle within twelve inches (12") of the regularly established curb line; except, that upon those streets that have been marked for angle parking, vehicles shall be parked at the angle to the curb indicated by such marks. (1965 Code § 10-10-6)