(1) The county board shall appoint a board of adjustment which shall consist of five members, plus one additional member designated as an alternate who shall attend and serve only when one of the regular members is unable to attend for any reason, each to be appointed for a term of three years and be removable for cause by the appointing authority upon written charges and after public hearing. No member of the board of adjustment shall be a member of the county board of commissioners or county board of supervisors. Vacancies shall be filled for the unexpired term of any member whose term becomes vacant. One member only of the board of adjustment shall be appointed by the county board from the membership of the county planning commission, and the loss of membership on the planning commission by such member shall also result in his immediate loss of membership on the board of adjustment and the appointment of another planning commissioner to the board of adjustment.

(2) The board of adjustment shall adopt rules in accordance with the provisions of any resolution adopted pursuant to sections 23-114 to 23-114.05, 23-168.01 to 23-168.04, 23-172 to 23-174, 23-174.02, 23-373, and 23-376. 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 each 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 with the county clerk and shall be a public record.