...∠AOD是∠AOC的补角,且∠BOC=1/2∠BOD,求∠AOC和∠BOD的度数?_百度...
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解：∠AOC+∠AOB=90°
∠AOB=∠AOC-1/2∠BOD
∴2∠AOC-1/2∠BOD=90°...........(1)
又∠AOC+∠AOD=180°
∠AOD=∠AOC+1/2∠BOD
∴2∠AOC+1/2∠BOD=180°..........(2)
(2)-(1)得∠BOD=90°
由（1）得∠AOC=1/2（90°+1/2∠BOD）=1/2（90°+1/2×90°）=67.5°
答：∠BOD=90°，∠AOC=67.5°
