A petition requesting the annexation of a defined area that is signed by a majority in value of the owners of land in the defined area, as shown by the tax rolls of the county or counties in which that area is located, that is signed by 50 landowners if the number of landowners is more than 50, that is signed by the single landowner of 2,000 or more acres of land in the area, or that is signed by a majority of the governing body of a municipal district, a county, or a city requesting annexation shall be filed with the secretary of the board.