点E在AC上,点F在AB上,BE、CF交于点O,且角C减角B等于20度,角EOF减角A等于70度,求角C的度数

Question

点E在AC上,点F在AB上,BE、CF交于点O,且角C减角B等于20度,角EOF减角A等于70度,求角C的度数

Answer 1

∠EOF=∠C+∠OEC=∠B+∠OFB
∠C-∠B=20°
得∠OFB-∠OEC=20°
∠AFO=180°-∠OFB=160°-∠OEC
∠AEO=180°-∠OEC
又有∠EOF-∠A=70°
由∠A+∠EOF+∠AFO+∠AEO=360°
得∠EOF-70°+∠EOF+160°-∠OEC+180°-∠OEC=360°
即2∠EOF-2∠OEC=90°
又有∠EOF=∠OEC+∠C
代入得2∠OEC+2∠C-2∠OEC=90°
∠C=45°