在三角形ABC中，AB＝AC，BD平分∠ABC，交AC于D点，若BD＝BC，则∠A等于多少度？
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∵ 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°
∴ ∠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°
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