已知∠AOB=3∠BOC,若∠BOC=30°,则∠AOC等于( ) A.120° B.120°或60° C.30° D.30°或90°
问题描述:
已知∠AOB=3∠BOC,若∠BOC=30°,则∠AOC等于( )
A. 120°
B. 120°或60°
C. 30°
D. 30°或90°
答
∵∠BOC=30°,∠AOB=3∠BOC,
∴∠AOB=3×30°=90°
(1)当OC在∠AOB的外侧时,
∠AOC=∠AOB+∠BOC=90°+30°=120度;
(2)当OC在∠AOB的内侧时,
∠AOC=∠AOB-∠BOC=90°-30°=60度.
故选:B.