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如图1所示,求角A+角B+角c+角D+角E+角F
http://hiphotos.baidu.com/zhidao/pic/item/d8f9d72a252e310fd42af1fd.jpg...
https://gss0.baidu.com/7LsWdDW5_xN3otqbppnN2DJv/zhidao/pic/item/d8f9d72a252e310fd42af1fd.jpg
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延长DE,AF交BC于M,N
则∠A+∠B=180°-∠ANB
∠C+∠D=180°-∠CMD
∠E=180°-∠MEF
∠F=180°-∠NFE
∴∠A+∠B+∠C+∠D+∠E+∠F=720°-(∠ANB+∠CMD+∠MEF+∠NFE)=720°-360°=360°
则∠A+∠B=180°-∠ANB
∠C+∠D=180°-∠CMD
∠E=180°-∠MEF
∠F=180°-∠NFE
∴∠A+∠B+∠C+∠D+∠E+∠F=720°-(∠ANB+∠CMD+∠MEF+∠NFE)=720°-360°=360°
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