Question

已知矩形ABCD的对角线AC和BD交于点O,在BC上取BE=BO,若∠BOE=75°,求∠CAE

Answer 1

∠BOE=75°,BE=BO =>∠DBC=30°

=>∠ABD=∠BAC=60°

所以,三角形ABO是个等边三角形

=>AB=OB=BE =>三角形ABE是个等腰直角三角形

=>∠BAE=45°

=>∠CAE=60°-45°=15°