如下图,已知∠AOC=60°,∠BOD=90°,∠AOB是∠DOC的3倍,求∠AOB的度数.http://www.baidu.com/s?wd=%C8%E7%CF%C2%CD%BC%2C%D2%D1%D6%AA%A1%CFAOC%3D60%A1%E3%2C%A1%CFBOD%3D90%A1%E3%2C%A1%CFAOB%CA%C7%A1%CFDOC%B5%C43%B1%B6%2C%C7%F3%A1%CFAOB%B5%C4%B
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/06 17:46:33
![如下图,已知∠AOC=60°,∠BOD=90°,∠AOB是∠DOC的3倍,求∠AOB的度数.http://www.baidu.com/s?wd=%C8%E7%CF%C2%CD%BC%2C%D2%D1%D6%AA%A1%CFAOC%3D60%A1%E3%2C%A1%CFBOD%3D90%A1%E3%2C%A1%CFAOB%CA%C7%A1%CFDOC%B5%C43%B1%B6%2C%C7%F3%A1%CFAOB%B5%C4%B](/uploads/image/z/5375531-11-1.jpg?t=%E5%A6%82%E4%B8%8B%E5%9B%BE%2C%E5%B7%B2%E7%9F%A5%E2%88%A0AOC%3D60%C2%B0%2C%E2%88%A0BOD%3D90%C2%B0%2C%E2%88%A0AOB%E6%98%AF%E2%88%A0DOC%E7%9A%843%E5%80%8D%2C%E6%B1%82%E2%88%A0AOB%E7%9A%84%E5%BA%A6%E6%95%B0.http%3A%2F%2Fwww.baidu.com%2Fs%3Fwd%3D%25C8%25E7%25CF%25C2%25CD%25BC%252C%25D2%25D1%25D6%25AA%25A1%25CFAOC%253D60%25A1%25E3%252C%25A1%25CFBOD%253D90%25A1%25E3%252C%25A1%25CFAOB%25CA%25C7%25A1%25CFDOC%25B5%25C43%25B1%25B6%252C%25C7%25F3%25A1%25CFAOB%25B5%25C4%25B)
如下图,已知∠AOC=60°,∠BOD=90°,∠AOB是∠DOC的3倍,求∠AOB的度数.http://www.baidu.com/s?wd=%C8%E7%CF%C2%CD%BC%2C%D2%D1%D6%AA%A1%CFAOC%3D60%A1%E3%2C%A1%CFBOD%3D90%A1%E3%2C%A1%CFAOB%CA%C7%A1%CFDOC%B5%C43%B1%B6%2C%C7%F3%A1%CFAOB%B5%C4%B
如下图,已知∠AOC=60°,∠BOD=90°,∠AOB是∠DOC的3倍,求∠AOB的度数.
http://www.baidu.com/s?wd=%C8%E7%CF%C2%CD%BC%2C%D2%D1%D6%AA%A1%CFAOC%3D60%A1%E3%2C%A1%CFBOD%3D90%A1%E3%2C%A1%CFAOB%CA%C7%A1%CFDOC%B5%C43%B1%B6%2C%C7%F3%A1%CFAOB%B5%C4%B6%C8%CA%FD&=%B0%D9%B6%C8%CB%D1%CB%F7&tn=360se_1_dg
如下图,已知∠AOC=60°,∠BOD=90°,∠AOB是∠DOC的3倍,求∠AOB的度数.http://www.baidu.com/s?wd=%C8%E7%CF%C2%CD%BC%2C%D2%D1%D6%AA%A1%CFAOC%3D60%A1%E3%2C%A1%CFBOD%3D90%A1%E3%2C%A1%CFAOB%CA%C7%A1%CFDOC%B5%C43%B1%B6%2C%C7%F3%A1%CFAOB%B5%C4%B
设∠DOC=a,则∠AOB=3a
因为∠AOC=60°
所以∠AOD=60°-a
又因为∠BOD=90°
所以∠COB=90°-a
根据图可知60°-a+a+90°-a=3a
解得a=75°/2
所以∠AOB=225°/2
设∠COD=x,则∠AOB=3x
因为∠BOC=∠AOB+∠AOC+∠DOC=90°
所以∠AOB=90°-60°-3X=X
所以4x=30°
x=7.5°
3x=7.5×3=22.5°
即∠AOB=22.5°
设∠COD=x,则∠AOB=3x
∵∠BOC=∠AOB+∠AOC+∠DOC=90°
∴∠AOB=90°-60°-3X=X
∴4x=30°
x=7.5°
3x=7.5×3=22.5°
∴∠AOB=22.5°