Question

△ABC的三条角平分线分别为AD,BE,CF,则∠ACF+∠CBE+∠DAC=?

Answer 1

90°.

∠ACF=1/2∠ACB,∠CBE=1/2∠ABC,∠DAC=1/2∠BAC

∠ACB+∠ABC+∠BAC=180°

所以∠ACF+∠CBE+∠DAC=1/2×180°=90°