如图 直线AB CD相交于点O OE平分∠BOD 且∠AOC=∠AOD-80° 求∠AOE的度数.

问题补充：

如图,直线AB,CD相交于点O,OE平分∠BOD,且∠AOC=∠AOD-80°,求∠AOE的度数.

答案：

.∠AOC + ∠AOD = 180°

∠AOC=∠AOD-80°

解得：∠AOC = 50°,∠AOD = 130°

∠DOE = 1/2 * ∠BOD = 1/2 * ∠AOC = 25°

∠AOE = ∠AOD + ∠DOE = 155°