Question

如图,直线AB、CD、EF都过点O,且EF⊥AB,OG平分∠EOD,若∠AOC=32°,求∠GOF的度数.

Answer 1

(1)OC在∠AOF内.∵∠BOD=∠AOC ∠AOC=28∴∠BOD=28°∵EF⊥AB∴∠BOE=90°

∴∠DOE=∠BOE-∠BOD=62°∵OG平分∠EOD∴∠EOG=1/2∠DOE=31°∴∠GOF=180°-∠EOG=149°

(2)OC在∠AOE内.∵∠BOD=∠AOC ∠AOC=28∴∠BOD=28°∵EF⊥AB∴∠BOE=90°

∴∠DOE=∠BOE+∠BOD=118°∵OG平分∠EOD∴∠EOG=1/2∠DOE=59°∴∠GOF=180°-∠EOG=121°