Question

如图,AB‖DE,∠a:∠D:∠B=2:3:4求∠a

积蓄答案啊

Answer 1

设∠a=2x, ∠D=3x ,∠B=4x
因为AB‖DE,
所以∠BCG=180-4x ,∠DCF=180-3x
因为∠BCG+∠a+∠DCF=180
所以180-4x +2x+180-3x=180
所以x=36

Answer 2

1. 按照如图做辅助线FG‖DE,则:∠B+∠GCB=180°，∠D+∠DCF=180°

2. ∠GCB+∠a+∠DCF=180°

3. 由以上3个式子可得∠B+∠D-∠a=180°，设∠a=2m;则m=36°

4. ∠a=72°

Answer 3

设∠a=2x, ∠D=3x ,∠B=4x
∵AB‖DE,
∴∠BCG=180-4x ,∠DCF=180-3x
∵∠BCG+∠a+∠DCF=180
∴180-4x +2x+180-3x=180
即x=36

Answer 4

1. 按照如图做辅助线FG‖DE,则:∠B+∠GCB=180°，∠D+∠DCF=180°

2. ∠GCB+∠a+∠DCF=180°

3. 由以上3个式子可得∠B+∠D-∠a=180°，设∠a=2m;则m=36°

4. ∠a=72°