The City shall have the power to provide for the alteration and extension of its boundaries, and to annex or detach territories pursuant to the authority conferred by the Constitution and laws of the State of Texas. Annexation is restricted to area adjacent to the City and within the City’s extra-territorial jurisdiction, except where the City owns the area to be annexed. Annexation may be initiated by either of the following methods:
(A) by petition of a majority of the qualified voters who are inhabitants of an area defined by the City Council; or if there are no qualified voters who are inhabitants of the area, by petition of persons owning a majority of the land in the area; or
(B) by action of the City Council, with or without the consent of the inhabitants or owners of the territory to be annexed.