Question

如图,AB,CD,EF相交于点O,EF⊥AB,OG为∠COF的平分线,OH为∠DOG的平分线,若∠AOC:∠COG=4:

Answer 1

设∠AOC＝4X

∵∠AOC：∠COG＝4：7,∠AOC＝4X

∴∠COG＝7X

∵OG平分∠COF

∴∠COF＝2∠COG＝14X

∵EF⊥AB

∴∠AOF＝90

∴∠AOC+∠COF＝90

∴4X+14X＝90

X＝5

∴∠AOC＝4X＝20,∠COF＝14X＝70,∠COG＝7X＝35

∴∠DOF＝180-∠COF＝180-70＝110°

∠DOG＝180-∠COG＝180-35＝145

∵OH平分∠DOG

∴∠DOH＝∠DOG/2＝72.5°