如图,在直角梯形ABCD中,AD‖BC,AB=DC=AD,AC⊥AB,将CB延长致点F,使BF=CD 求∠ABC的度数
问题描述：
如图,在直角梯形ABCD中,AD‖BC,AB=DC=AD,AC⊥AB,将CB延长致点F,使BF=CD 求∠ABC的度数
答
∵AB = CD
∴∠ABC = ∠DCB
∵AD = DC
∴∠DAC = ∠DCA
∵AD//BC
∴∠DAC = ∠ACB
∴AC是∠DCB的角平分线
∵∠ABC = ∠DCB
∴∠ABC ：∠ACB = 2：1
∵AC ⊥ AB
∴∠ABC = 60°,∠ACB = 30°