When any part of the territory embracing a school under the supervision and control of the county board of education is annexed to a city having a city board of education by extension of the corporate limits of such city, the county board of education shall retain supervision and control of said school and for school purposes shall retain the same control of the territory and revenues which it exercised prior to such annexation, for the purpose of using and devoting said school to the benefit of all children who were or would be entitled to the use and benefit of the school so long as it was a county school, until an agreement has been made between the county board of education and the city board of education, and the city council or commission or other governing body of the city to which the territory was annexed, with reference to the matter of existing indebtedness and of providing the same or equivalent school facilities for the children in that part of the territory in the school district or districts not annexed or made a part of such city.