Question

如图，在△ABC中，AB＝AC，BD平分∠ABC，交AC于点D，若BD＝BC，则∠A等于多少度

Answer 1

答案是36度
AB=AC 推出＜Abc=＜Acb
BD平分<ABc 推出<ABD=<DBc推出<ABc=2<DBc
推出<ACB=2<DBc
BD=Bc推出<BDc=<BcD=2<DBC
在三角形DBc里5<DBc=18O推出<A=36度

Answer 2

∵ AB＝AC
∴ ∠A+2∠ABC = 180
∠ABC = (180 - ∠A) /2 = 90 -1/2∠A

∵ BD＝BC
∴ ∠CBD+2∠BDC = 180
∵ BD平分∠ABC ∠BDC=∠A+∠ABD = ∠A+1/2∠ABC
1/2∠ABC+2(∠A+1/2∠ABC ) = 180
∠ABC = 2/3(180 - 2∠A) = 120 - 4/3∠A

∴ 90 -1/2∠A = 120 - 4/3∠A
∠A = 36°