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.

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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.
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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.
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.

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.
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