Question

已知：如图,△ABC中,AB=AC,D是AC上一点,DA=DB=BC,求∠A的度数

Answer 1

∵AB=AC

∴∠ABC=∠C

∵DA=DB=BC

∴∠A=∠DBA ,∠C=∠BDC

∵∠DBA+∠A=∠BDC

∴∠BDC=2∠A

∵∠ABC=∠C,∠C=∠BDC

∴∠ABC=∠C=2∠A

∵∠ABC+∠C+∠A=180

2∠A+2∠A+∠A=180

5∠A=180

∠A=36