OC垂直于OB,垂足为O,角COB与角AOC之差为60度.若将“角COB与角AOC之差为60度”省去,

题目

OC垂直于OB,垂足为O,角COB与角AOC之差为60度.若将“角COB与角AOC之差为60度”省去,
且已知角COB：角AOC=3:1,试求角AOB的度数.

答案

易得：∠COB=90°
∠AOC=30°
当∠AOC在∠BOC内部时：∠AOB=∠BOC-∠AOC=90°-30°=60°
当∠AOC在∠BOC外部时：∠AOB=∠BOC+∠AOC=90°+30°=120°