如图所示,求角A+角B+角C+角D+角E+角F的值.

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如图所示,求角A+角B+角C+角D+角E+角F的值.
如图所示,求角A+角B+角C+角D+角E+角F的值.

如图所示,求角A+角B+角C+角D+角E+角F的值.
延长AF交点CD于点G
则∠AGC=∠D+∠DOG
∵∠DOG=∠E+∠F
∴∠AGC=∠E+∠F+∠D
∵∠A+∠B+∠C+∠AGC=360°
∴∠A+∠B+∠C+∠E+∠F+∠D=360°

角A+角B+角C+角D+角E+角F=360°
连AD, 则∠E+∠F=∠FAD+∠EDA
∴角A+角B+角C+角D+角E+角F刚好等于四边形ABCD四内角和=360°

360

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