延长BD至点E,作DE=CD,连接AE
∵∠ABD＝60°,∠ADB＝76°
∴∠DAB＝180°－60°－76°＝44°
∵∠BDC=28°,∠ADB=76°
∴∠ADC＝∠BDC＋∠ADB＝28°＋76°＝104°
∵∠ADE+∠ADB=180°,∠ADB=76°
∴∠ADE=104°
∴∠ADC=∠ADE
∵AD=AD,DE=CD
∴△ADC≌△ADE
∴AC=AE
∵AB=AC
∴AB=AE
∴∠ABD=∠AEB
∵∠ABD=60°
∴∠AEB=60°
∵∠BAE+∠ABD+∠AEB=180°
∴∠BAE=60°
∵∠BAD=44°
∴∠DAE=16°
∵△ADC≌△ADE
∴∠DAC=∠DAE=16°
∴∠BAC=28°
∵AB=AC
∴∠ABC=∠ACB
∵∠BAC+∠ABC+∠ACB=180°
∴∠ABC=∠ACB=76°
∵∠DBC+∠ABD=∠ABC
∴∠DBC=∠ABC-∠ABD=76°－60°=16°