Tex. Local Government Code § 231.178

(a) The commissioners court may provide for the appointment of a board of adjustment. In the regulations adopted under this subchapter, the commissioners court may authorize the board of adjustment, in appropriate cases and subject to appropriate conditions and safeguards, to make special exceptions to the terms of the regulations that are consistent with the general purpose and intent of the regulations and in accordance with any applicable rules contained in the regulations.

(b) A board of adjustment must consist of five members to be appointed for staggered terms of two years. The appointing authority may remove a board member for cause on a written charge after a public hearing. A vacancy on the board shall be filled for the unexpired term.

(c) The board shall adopt rules in accordance with any order adopted under this subchapter. Meetings of the board are held at the call of the chairman and at other times as determined by the board. The chairman or acting chairman may administer oaths and compel the attendance of witnesses. All meetings of the board shall be open to the public.

(d) The board shall keep minutes of its proceedings that indicate the vote of each member on each question or indicate that a member is absent or fails to vote. The board shall keep records of its examinations and other official actions. The minutes and records shall be filed immediately in the board's office and are public records.