The City Council shall have power by ordinance to fix the boundary limits of Harker Heights; and to provide for the extension of said boundary limits and the annexation of additional territory lying adjacent to said City, or relinquishment of any territory within the City, with or without the consent of the territory and inhabitants annexed or relinquished. Upon the introduction of such an ordinance in the City Council, it shall be published one time in a newspaper of general circulation in the City of Harker Heights, and shall not thereafter be finally acted upon until at least thirty days have elapsed after such publication thereof. Any citizen of Harker Heights, or of the territory to be annexed, or relinquished, shall have the right to contest said annexation or relinquishment by filing with the City Council a written petition setting out their reasons for said contest and after citizen or citizens shall have been given an opportunity to be heard, said ordinance, in original or amended form, as said City Council in its judgment may determine, may be finally passed, and the territory so annexed shall be a part of Harker Heights and 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 said city, and the inhabitants of the territory so relinquished shall forfeit said rights and privileges.