A petition describing the territory proposed to be annexed and requesting that proceedings be taken for its annexation shall be signed by all of the owners of the real property described therein, verified by the affidavit of one of the petitioners, addressed to the board, and filed with the secretary of the district. If a portion of the territory consists of public highways, streets, roads or paths, it shall not be necessary to secure the signatures to the petition of the owners only of the real property occupied by such public highways, streets, roads or paths.