Such local legislative body shall provide for the appointment of a board of adjustment, and in the regulations and restrictions adopted pursuant to the authority of sections 89.010 to 89.140 may provide that the board of adjustment may determine and vary their application in harmony with their general purpose and intent and in accordance with general or specific rules therein contained. The board of adjustment shall consist of five members, who shall be residents of the municipality except as provided in section 305.410. The membership of the first board appointed shall serve respectively, one for one year, one for two years, one for three years, one for four years, and one for five years. Thereafter members shall be appointed for terms of five years each. Three alternate members may be appointed to serve in the absence of or the disqualification of the regular members. All members and alternates shall be removable for cause by the appointing authority upon written charges and after public hearing. Vacancies shall be filled for the unexpired term of any member whose term becomes vacant. The board shall elect its own chairman who shall serve for one year. The board shall adopt rules in accordance with the provisions of any ordinance adopted pursuant to sections 89.010 to 89.140. Meetings of the board shall be held at the call of the chairman and at such other times as the board may determine. Such chairman, or in his absence the acting chairman, may administer oaths and compel the attendance of witnesses. All meetings of the board shall be open to the public. The board shall keep minutes of its proceedings, showing the vote of each member upon question, or, if absent or failing to vote, indicating such fact, and shall keep records of its examinations and other official actions, all of which shall be immediately filed in the office of the board and shall be a public record. All testimony, objections thereto and rulings thereon, shall be taken down by a reporter employed by the board for that purpose.