设∠A=x,则∠ABC=∠C=2x
∠A+∠ABc+∠C=180°
所以：x+2x+2x=180°
x=36°
∠ABC=2x=72°
又因为：BD是∠ABC的平分线
所以：∠ABD=∠ABC÷2=72°÷2=36°
∠ADB=180°-∠A-∠ABD
         =180°-36°-36°=108°
答：∠A的度数是36°,∠ADB的度数是108°