Question

如图所示;在△ABC中,D在BC上,若AD=BD,AB=AC=CD,求∠BAC的度数

Answer 1

因为AD=BD,所以∠ABD=∠DBA
又因为AB=AC,所以∠ABD=∠ACB
还有，AC=CD,所以∠DAC=∠ADC
据以上可得：∠ABD=∠ACD
据三角形的外角定理可得,∠DAC=∠ADC=∠DAB+∠ABD=2∠ACD
∠DAC+∠ADC+∠ACD=180°
即5∠ACD=180°
∠ACD=36°
∠BAC=∠BAD+∠DAC=∠BAD+∠ADC=3∠ACD=108°

Answer 2

设ABC为α那么BAD=ACB=α根据三角形内角和是180°,(180-α)/2+3α=180得出答案是36°