Question

如图,AB=AC,AD=BD,CB=CD,求∠ABC的度数

Answer 1

∵CB=CD

∴∠CBD=∠CDB

∵AD=BD

∴∠A=∠DBA

∵AB=AC

∴∠ABC=∠C

∵∠CDB=∠A+∠DBA=2∠A

∴∠ABC=∠DBA+∠CBD=∠A+2∠A=3∠A

∴∠ACB=∠ABC=3∠A

∵∠A+∠ABC+∠ACB=180°

∴∠A+3∠A+3∠A=180°

∠A=180°/7

∴∠ABC=3∠A=540°/7