Question

如图所示,OB平分∠AOC,且∠BOC:∠COD=2:5,∠AOD-∠COB=30° 求∠BOC，∠COD，∠AOD的度数。

Answer 1

∵∠BOC:∠COD=2:5,则可设
∠BOC=2x ∠COD=5x
,又OB平分∠AOC
则∠BOC=∠AOB=2x
又∠AOD-∠COB=30°
,则∠AOD=∠COB+30°=2x+30°
∵∠AOB+∠BOC+∠COD+∠AOD=360°
∴2x+2X+5X+2X+30°=360°
求得x=30°
∴∠BOC=60°，∠COD=150°，∠AOD=90°

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Answer 2

∵∠BOC:∠COD=2:5,则可设
∠BOC=2x ∠COD=5x
,又OB平分∠AOC
则∠BOC=∠AOB=2x
又∠AOD-∠COB=30°
,则∠AOD=∠COB+30°=2x+30°
∵∠AOB+∠BOC+∠COD+∠AOD=360°
∴2x+2X+5X+2X+30°=360°
求得x=30°
∴∠BOC=60°，∠COD=150°，∠AOD=90°

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Answer 3

∵∠BOC:∠COD=2:5,则可设
∠BOC=2x ∠COD=5x
,又OB平分∠AOC
则∠BOC=∠AOB=2x
又∠AOD-∠COB=30°
,则∠AOD=∠COB+30°=2x+30°
∵∠AOB+∠BOC+∠COD+∠AOD=360°
∴2x+2X+5X+2X+30°=360°
求得x=30°
∴∠BOC=60°，∠COD=150°，∠AOD=90°

Answer 4

60 150

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