Question

 如图，已知∠1 +∠2 =180°，∠DEF =∠A，求证：∠ACB = ∠DEB．

Answer

见解析

【解析】证明：∵ ，     ∴······ 2分

∴ EF∥AB·································· 3分

∴ ∠DEF =∠BDE······························· 4分

∵ ∠DEF=∠A

∴ ∠BDE =∠A································ 6分

∴ DE∥AC·································· 7分

∴ ∠ACB =∠DEB 8分

利用平角可求得EF∥AB，从而求得DE∥AC，最后得出结论