如图,△ABC中,∠C=70°,AD是∠CAB的平分线,BD是△ABC的外角平分线,AD与BD交于D,求∠D的度数._数学解答

如图,△ABC中,∠C=70°,AD是∠CAB的平分线,BD是△ABC的外角平分线,AD与BD交于D,求∠D的度数.

人气：152 ℃　时间：2020-04-02 11:27:23

解答

∵AD是∠CAB的平分线
∴∠BAD=1/2∠BAC
∵∠DBC=1/2(180°-∠ABC)=90°-1/2∠ABC
∴∠D=180°-(∠BAD+∠ABC+∠DBC)
=180°-(1/2∠BAC+∠ABC+90°-1/2∠ABC)
=90°-1/2(∠BAC+∠ABC)
=90°-1/2(180°-∠C)
=1/2∠C
=35°