Question

如图所示，直线AB，CD相交于点O，OE平分∠BOD，且∠AOC＝∠COB－30°，则∠AOE=

Answer 1

设∠AOC=x
根据题意有
x+x/2+x/2+2(x+30°)=360°
x=50°
∠AOC=50°

追答

∠AOC+∠COB=180
∠COB-∠AOC=30°
∠AOC=(180-30)/2=75°
∠AOD=∠COB=∠AOC+15=90°
∠AOE=∠AOD+∠DOE
=∠AOD+1/2∠BOD
=∠AOD+1/2∠AOC=90+1/2*75=127.5°