Proceedings may be commenced for the annexation of territory to an existing district by petition filed with the county clerk and signed by registered voters residing within the territory to be annexed equal in number to at least eight percent of the number of votes cast in the territory proposed to be annexed for the office of Governor at the last general election at which a Governor was elected. If both incorporated and unincorporated territory are included within the new territory, the petition shall be signed by registered voters equal in number in each territory to at least eight percent of the votes so cast therein for Governor.