Upon the making of any such agreement, the board shall be empowered and it shall be its duty to cause such examination and appraisal to be made as will determine the area and value, as nearly as may be, of the lands lost to the state, or the title to, use or possession of which is claimed by the United States by reason of the causes mentioned in RCW
79.02.120, and proposed to be relinquished to the United States, and shall cause an examination and appraisal to be made of any lands which may be designated by the officers of the United States as subject to selection by the state in lieu of the lands aforesaid, to the end that the state shall obtain lands in lieu thereof of equal area and value.