在AB的延长线上取一点E,在AC的延长线上取一点F
∠A+∠ABC=∠BCF ∠A+∠ACB=∠CBE
则∠A+（∠A+∠ABC+∠ACB）=∠A+180°=∠BCF+∠CBE
∠BCF+∠CBE=2（∠CBD+∠BCD）=2(180°-∠D)
则）∠A+180°=2(180°-∠D)
∠A+2∠D=180°