∠BAF,∠CBD,∠ACE是△ABC的三个外角,求∠BAF+∠CBD+∠ACE的度数.

问题描述:

∠BAF,∠CBD,∠ACE是△ABC的三个外角,求∠BAF+∠CBD+∠ACE的度数.

∵∠BAF=180-∠BAC,∠CBD=180-∠ABC,∠ACE=180-∠ACB
∴∠BAF+∠CBD+∠ACE
=180-∠BAC+180-∠ABC+180-∠ACB
=540-(∠BAC+∠ABC+∠ACB)
∵∠BAC+∠ABC+∠ACB=180
∴∠BAF+∠CBD+∠ACE=540-180=360°