如图,AB=AC,AB的垂直平分线交AC于D点,若AD=BC,∠ABC=72°,点E在BC的延长线上,且CE=CD连AE,求∠CAE

18°
AB=AC,∠ABC=72°,则∠ACB=72°,∠BAC=36°,
D为AB中垂线上一点,则连DB,则DA=DB,∠DBA=36°,∠DBC=36°
因AD=BC,DA=DB=BC,∠CDB=72°
CE=CD,∠CDE=∠CED=36°=∠CBD
则DE=DB=BC=AD
则∠DAE=∠DEA=36°/2=18°