①∵∠ABC=40°,∠ACB=70°, ∴∠BAC=180°-∠ABC-∠ACB=70°, ∵AD平分∠BAC, ∴∠CAD=∠BAC=×70°=35°, ∵AE⊥BC, ∴∠AEC=90°, ∵∠C=70°, ∴∠EAC=180°-90°-70°=20°, ∴∠DAE=∠DAC-∠EAC=35°-20°=15°.
②∵∠ABC=30°,∠ACB=110°, ∴∠BAC=180°-∠ABC-∠ACB=40°, ∵AD平分∠BAC, ∴∠CAD=∠BAC=×40°=20°, ∵AE⊥BC, ∴∠AEC=90°, ∵∠C=110°, ∴∠EAC=∠ACB-∠AEC=110°-90°=20°, ∴∠DAE=∠DAC+∠EAC=20°+20°=40°.
③∠DAE=∠ACB-∠ABC,理由如下: 分为两种情况:如图1, ∠BAC=180°-(∠ABC+∠ACB), ∵AD平分∠BAC, ∴∠DAC=[180°-(∠ABC+∠ACB)]=90°-∠ABC-∠ACB, ∵AE⊥BC, ∴∠AEC=90°, ∴∠CAE=90°-∠ACB, ∴∠DAE=∠DAC-∠EAC=(90°-∠ABC-∠ACB)-(90°-∠ACB)=∠ACB-∠ABC; 如图2, ∠BAC=180°-∠ABC-∠ACB, ∵AD平分∠BAC, ∴∠CAD=∠BAC=×(180°-∠ABC-∠ACB)=90°-∠ABC-∠ACB, ∵AE⊥BC, ∴∠AEC=90°, ∴∠EAC=∠ACB-∠AEC=∠ACB-90°, ∴∠DAE=∠DAC+∠CAD=90°-∠ABC-∠ACB+∠ACB-90°=∠ACB-∠ABC. |