如图,等腰三角形abc中,ab=ac,bd是三角形abc的角平分线ad=bd=bc,求角a的度数

AB=AC,则∠ABC=∠C.
(1)当AD=BD;BD=BC时:∠DBA=∠A,设∠DBA=∠A=X(度),则∠BDC=2X.
∴∠C=∠BDC=2X=∠ABC.
∠A+∠ABC+∠C=180°,即:X+2X+2X=180,X=36.即∠A=36°.
(2)当AD=BD;CD=BC时:设∠DBA=∠A=X(度),则∠BDC=2X=∠DBC.
∴∠ABC=∠DBA+∠DBC=3X=∠C.
∠A+∠ABC+∠C=180°,即:X+3X+3X=180,X=180/7.即∠A=(180/7)°.