如图,△ABC中,∠BAC=120°,AD⊥BC于D,且AB+BD=DC,则∠C的大小是(  ) A.20° B.25° C.30° D.大于30°

问题描述:

如图,△ABC中,∠BAC=120°,AD⊥BC于D,且AB+BD=DC,则∠C的大小是(  )
A. 20°
B. 25°
C. 30°
D. 大于30°

如图,在DC上取DE=DB.连接AE,在Rt△ABD和Rt△AED中,BD=ED,AD=AD.∴△ABD≌△AED.∴AB=AE,∠B=∠AED.又∵AB+BD=CD∴EC=CD-DE=CD-BD=(AB+BD)-BD=AB=AE,即EC=AE,∴∠C=∠CAE∴∠B=∠AED=2∠C又∵∠B+∠C=18...