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已知:如图,∠1+∠2=180°,∠3=∠B,试判断∠AED与∠C的大小关系,并说明理由.

解:∠C与∠AED相等,理由如下:

∵∠1+∠2=180°(                  ▲                  ),

∠1+∠DFE=180°(                  ▲                  ),

∴∠2=                  ▲                                    ▲                  ),

∴ABEF(                  ▲                  ),

∴∠3=∠ADE(                  ▲                  ).

又∠B=∠3(                  ▲                  ),

∴∠B=∠ADE,

∴DEBC(                  ▲                  ),

∴∠C=∠AED(                  ▲                  ).

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