The City Commission shall have the power by Ordinance to fix the boundary limits of the City of Port Isabel and to provide for the extension of boundary limits and the annexation of additional territory lying adjacent to said City, all pursuant to and in conformance with the procedure provided for in Article 970a of the Revised Civil Statutes of Texas, including all subsequent amendments thereto, and any other applicable State Statutes. Upon additional territory being so annexed, the inhabitants thereof shall be entitled to all rights, and privileges of other citizens; and shall be bound by the Acts, Ordinances, Resolutions and Regulations of the City of Port Isabel.