Question

9.如图，OC是∠AOB的平分线，OE是∠AOD的平分线， 若∠BOD=50°,求∠COE的度数。.

Answer 1

∠BOD=∠AOB - ∠AOD = 50°
OC是∠AOB的平分线，∠AOC =∠AOB /2
OE是∠AOD的平分线，∠AOE = ∠AOD /2
∠COE=∠AOC - ∠AOE =∠AOB /2 - ∠AOD /2= 50°/2 = 25°

此方法最简单，好理解
祝你学习进步，更上一层楼！ (*^__^*)

Answer 2

设∠AOE=x
∵OE平分∠AOD
∴∠AOD=2∠AOD
∴∠AOD=2x
∵∠BOD=50°
∠AOB=∠BOD+∠AOD
∴∠AOD=2x+50°
∵OC平分∠AOB
∴∠AOC=1/2∠AOB
∴∠AOC=x+25°
∵∠COE=∠AOC-∠AOE
∴∠COE=25°

Answer 3

∵OC平分∠AOB，
∴∠BOC=1/2∠AOB=1/2(∠BOD+∠AOD)=25°+1/2∠AOD，
∵OE平分∠AOD，∠DOE=1/2∠AOD，
∴∠COD=∠BOC-∠BOD=25°+1/2∠AOD-50°=1/2∠AOD-25°，
∴∠COE=∠DOE-∠COD=1/2∠AOD-(1/2∠AOD-25°)=25°。

Answer 4

解：设∠AOD=X°
∵OE是∠AOD的平分线∴∠AOE=1/2∠AOD=1/2X°
∵OC是∠AOB的平分线∴∠AOC=1/2∠AOB=1/2(∠AOD+∠BOD)=1/2(X+50)°
∴∠COE=∠AOC-∠AOE=1/2(X°+50°)-1/2X°=1/2X°+25°-1/2X°=25°