Question

如图,AB∥CD,已知∠BAF=3∠BAE,∠DCF=3∠DCE,试探讨∠AEC与∠AFC的数量关系,并给出证明.

Answer 1

连接EF,

∠AEC = ∠BAF/3 + ∠DCF/3

3∠AEC = ∠BAF + ∠DCF

∠AFC = (180度 - ∠BAF) + (180度 - ∠DCF)

= 360度 - (∠BAF + ∠DCF)

= 360度 - 3∠AEC

∠AFC + 3∠AEC = 360度

∠AEC = (360度 - ∠AFC) / 3