第1个回答 2019-07-25
∵AB=AC,∴∠ABC=∠C=1/2(180°-∠A)=90°-1/2∠A,
∵AD=BD,∴∠ABC=∠A,
∵BC=BD,∴∠BDC=∠C=90°-1/2∠A,
∠BDC=∠ABD+∠A=2∠A,
∴90°-1/2
∠A=2∠A,
∠A=36°,
∴∠ABC=∠C=72°,
第2个回答 2020-05-28
∠ABC=∠ACB=72°
∠BAC=36°
ab=ac
∠abc=∠acb
ad=bd
∠adb=∠dbd
bd=bc
∠dbc=∠dcb=∠dbd+∠adb
由
∠bca+∠dbd+∠acb=180
∠bca+∠abd+∠dbc+∠acb=180
即可得最上答案
第3个回答 2019-05-30
∵△ABC中,AD=BD=BC
∴∠A=∠1,∠2=∠C
∴∠2=∠A+∠1=2∠A
∴∠C=2∠A
又∵AB=AC
∴∠ABC=∠C
∴∠ABC=2∠A
又∵△ABC中,∠A+∠ABC+∠C=180°
即∠A+2∠A+2∠A=5∠A
=180°
∴∠A=36°
∴∠ABC=∠C=72°
第4个回答 2019-09-26
∵
AB=AC
∴∠C=∠ABC
∵
BD=BC
∴∠C=∠BDC
∵
DA=DB
∴∠A=∠ABD
∠A+∠ABC+∠C=180°
∠A+2∠C=180°
∠A+2∠BDC=180°
∠A+2(180°-∠ADB)=180°
∠A+360°-2∠ADB=180°
∠A+360°-2(180°-∠ABD-∠A)=180°
∠A+360°-2(180°-∠A-∠A)=180°
∠A+360°-360°+4∠A=180°
5∠A=180°
∠A=36°
∠B=∠C=(180-∠A)/2=72°