连接AE
∴∠BAE+∠AEF+∠B+∠F=360°
∵∠BAE=∠BAC+∠CAE
∠AEF=∠FED+∠AED
∠D+∠C=∠CAE+∠AED (有个对顶角相等)
∴∠BAC+∠C+∠C+∠AED+∠B+∠F=360°
即:∠A+∠B+∠C+∠D+∠E+∠F=360°
连接AE
∴∠BAE+∠AEF+∠B+∠F=360°
∵∠BAE=∠BAC+∠CAE
∠AEF=∠FED+∠AED
∠D+∠C=∠CAE+∠AED (有个对顶角相等)
∴∠BAC+∠C+∠C+∠AED+∠B+∠F=360°
即:∠A+∠B+∠C+∠D+∠E+∠F=360°