SDCL § 7-25A-14: Board members known as supervisors--Oath and term of office--Vacancies.

Members of the board shall be known as supervisors and, upon entering into office, shall take and subscribe to the oath of office as prescribed by law. They shall hold office for the terms for which they were elected or appointed and until their successors are chosen and qualified. If, during the term of office, a vacancy occurs, the remaining members of the board shall fill the vacancy by an appointment for the remainder of the unexpired term.