解：∵DA⊥AB∴∠A＝90∴∠ABD＝180-∠A-∠ADB＝180-90-50＝40∵BD平分∠ABC∴∠ABC＝2∠ABD＝80∵∠A+∠ABC+∠C+∠ADC＝360, ∠ADC＝∠ADB+∠BDC＝50+80＝130∴90+80+∠C+130＝360∴∠C＝60°
