Question

已知AB和CD相交于O，射线OB⊥AB于O，射线OF⊥CD于O，且∠BOF=25°，求∠AOC，∠EOD怎么做

Answer 1

解： 如图所示

     ∵OF⊥CD,∠BOF＝25°∠BOA为平角

     ∴∠AOC＝∠BOA－∠COF－∠BOF

                       ＝180°－90°－25°

             ＝65°

     ∵∠AOC与∠BOD为对顶角

     ∴∠BOD＝∠AOC＝65°

     ∵OE⊥AB ,∠BOD＝65°

°   ∴∠DOE＝∠BOE－∠BOD＝90°－65°＝25°

     ∴∠AOC＝＝65°,∠DOE＝25°