Question

已知o是直线ab上一点,角cod=120度,oe是角aoc的平分线,of是叫bod的角平分线,求角eof

Answer 1

∵直线AB

∴∠AOB＝180

∵∠AOB＝∠AOC+∠COD+∠BOD,∠COD＝120

∴180＝∠AOC+120+∠BOD

∴∠AOC+∠BOD＝60

∵OE平分∠AOC

∴∠COE＝∠AOC/2

∵OF平分∠BOD

∴∠DOF＝∠BOD/2

∴∠EOF＝∠COE+∠DOF+∠COD

＝∠AOC/2+∠BOD/2+∠COD

＝（∠AOC+∠BOD）/2+∠COD

＝60/2+120

＝150