Question

如圖，已知，BD是△ABC的角平分線，且AD=DB=BC，求△ABC的各個內角的度數．

Answer 1

∵BD=BC=AD，BD平分∠ABC，
∴∠C=∠BDC，∠A=∠ABD=∠CBD．
設∠A=x，則∠C=∠BDC=2x，∠ABC=2x．
則x+2x+2x=180°．
解得 x=36°．
則∠A=∠ABD=72°．
故∠A=36°，∠C=72°，∠ABC=72°．