The governing body of each such district shall be a board known as a high school board of trustees, which shall be constituted, when the boards of trustees of two or more school districts shall have acted in establishing or evidencing an intention to establish a high school pursuant to or under color of authority of any special act or any act making a special provision in or about the subject matter of a general act, in the manner provided in such act and in any other case in the manner provided in § 59-39-20.