解:設?$∠1$?的度數(shù)為?$x,$?則?$∠2$?的度數(shù)為?$x + 40°。$?
∵?$O$?是直線?$AB$?上一點,
∴?$∠1$?與?$∠2$?是鄰補角,即?$∠1 + ∠2 = 180°,$?
∴?$x + (x + 40°) = 180°,$?
?$ 2x = 180° - 40°,$?
?$ 2x = 140°,$?
?$ x = 70°。$?
∴?$∠1 = 70°,$??$∠2 = 70° + 40° = 110°。$?
答:?$∠1$?的度數(shù)為?$70°,$??$∠2$?的度數(shù)為?$110°。$?