解：∵∠A=1/2∠C=1/2∠ABC∴∠C=∠ABC=2∠A∵∠A+∠C+∠ABC=180°∴∠A+2∠A+2∠A=5∠A=180°∴∠A=36°∴∠C=∠ABC=72°∵BD平分∠ABC∴∠ABD=∠DBC=1/2∠ABC=36°∴∠BDC=180°-∠DBC-∠C=180°-36°-72°=72°
