Question

已知AB∥CD,FH平分∠EFD,GF⊥HF于F,∠AEF=62,求∠GFC

Answer 1

∵AB∥CD

∴∠EFD=∠AEF=62°

∵FH平分∠EFD

∴∠EFH=1/2∠EFD=1/2×62°=31°

∵GF⊥HF即∠GFH=90°

∴∠GFE=90°-∠EFH=90°-31°=59°

∵AB∥CD

∴∠AEF+∠EFC=180°

∴∠EFC=180°-∠AEF=180°-62°=118°

∴∠GFC=∠EFC-∠GFE=118°-59°=59°