1,在△ABC中,D,E分别是∠ACB与∠ABC的三等分线的交点,若∠ABC+∠ACB=120°,求∠CDE

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1,在△ABC中,D,E分别是∠ACB与∠ABC的三等分线的交点,若∠ABC+∠ACB=120°,求∠CDE
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1,在△ABC中,D,E分别是∠ACB与∠ABC的三等分线的交点,若∠ABC+∠ACB=120°,求∠CDE
1,在△ABC中,D,E分别是∠ACB与∠ABC的三等分线的交点,若∠ABC+∠ACB=120°,求∠CDE

1,在△ABC中,D,E分别是∠ACB与∠ABC的三等分线的交点,若∠ABC+∠ACB=120°,求∠CDE

∵在△BCD中,EC平分∠DCB,EB平分∠CBD
∴DE平分∠BDC
∵∠ A=60°,
∴∠ABC+∠ACB=180-60=120°
∵点D、E分别是<ACB与<ABC三等分线的交点
∴∠BCD=2/3∠ACB,∠CBD=2/3∠ABC
∴∠BCD+∠CBD=2/3*120°=80°
∴∠BCD=180-(∠BCD+∠CBD)=100°
∴∠CDE=50°

∵∠ C=∠ EC'F,∠C'EF=∠CEF,∠C'FE=∠CFE,
    ∠C'EF+∠EC'F+∠C'FE=180°,∠C'EF+∠1+∠C'FE+∠2+∠CEF+∠CFE=360°,
∴2∠C'EF+∠1+2∠C'FE+∠2=360°,2∠C'EF+2∠C'FE+2∠C=360°,
∴∠1+∠2=2∠ C