Question

如图,已知∠AOB和∠AOD的度数之比是2:11，∠AOC=∠DOB=90°，求∠AOB和∠BOC度数.

Answer 1

∠AOB=20，BOC=70;
AOB:AOD=AOB:(AOB+90)=2:11→(AOB+BOD)/AOB=11:2;
1+BOD/AOB=11/2
BOD:AOB=9:2
因BOD=90，则AOB=20
BOC=90-20=70

Answer 2

因为 ∠AOB+∠BOC=90°
∠COD+∠BOC=90°

所以得出∠AOB=∠COD

设∠AOB=∠COD=X ∠BOC=Y

可以列出两个方程 X/(2X+Y)=2/11
X+Y=90

解得X=20 Y=70 即∠AOB=20 ∠BOC=70

Answer 3

AOB:AOD=AOB:(AOB+90)=2:11→(AOB+BOD)/AOB=11:2;

1+BOD/AOB=11/2
BOD:AOB=9:2
因BOD=90，则AOB=20
BOC=90-20=70

Answer 4

AOB:AOD=AOB:(AOB+90)=2:11→(AOB+BOD)/AOB=11:2;
1+BOD/AOB=11/2
BOD:AOB=9:2
因BOD=90，则AOB=20
BOC=90-20=70