如图,在△ABC中,∠A=70°BD=BE,CD=CF则∠EDF=()
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如图,在△ABC中,∠A=70°BD=BE,CD=CF则∠EDF=()
![](http://img.wesiedu.com/upload/0/96/0962ebcf0de322c5af73690965eeacc3.jpg)
![](http://img.wesiedu.com/upload/0/96/0962ebcf0de322c5af73690965eeacc3.jpg)
![如图,在△ABC中,∠A=70°BD=BE,CD=CF则∠EDF=()](/uploads/image/z/19047589-61-9.jpg?t=%E5%A6%82%E5%9B%BE%2C%E5%9C%A8%E2%96%B3ABC%E4%B8%AD%2C%E2%88%A0A%3D70%C2%B0BD%3DBE%2CCD%3DCF%E5%88%99%E2%88%A0EDF%3D%28%29)
∠ABC+∠ACB=180°-∠A=110°
∵BD=BE,CD=CF
∴∠EDB+∠CDF
=(1/2)[(180°-∠ABC)+(180°-∠ACB)]
=(1/2)[360°-(∠ABC+∠ACB)]
=(1/2)[360°-110°]
=125°
∴∠EDF
=180°-(∠EDB+∠FDC)
=180°-125°
=55°
∵BD=BE,CD=CF
∴∠EDB+∠CDF
=(1/2)[(180°-∠ABC)+(180°-∠ACB)]
=(1/2)[360°-(∠ABC+∠ACB)]
=(1/2)[360°-110°]
=125°
∴∠EDF
=180°-(∠EDB+∠FDC)
=180°-125°
=55°
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