Question

如图,在△ABC中,点D、E、F分别在BC、AB、AC上,且BD=BE,CD=CF,∠EDF=40°,则∠A等于多少度?

Answer 1

∠EDF=40°

∠BDE+∠CDF=180°-40°=140°

∠B=180°-2∠BDE

∠C=180°-2∠CDF

∠B+∠C=360°-2(∠BDE+∠CDF)=360°-2*140°=80°

∠A=180°-(∠B+∠C)=180°-80°=100°