一道数学题.不是很难的.(1)如图,在△ABC中,∠ACB=100°,AC=AE,BC=BD,则∠DEC的度数为( )A.20° B.25° C.30° D.40°

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一道数学题.不是很难的.(1)如图,在△ABC中,∠ACB=100°,AC=AE,BC=BD,则∠DEC的度数为( )A.20° B.25° C.30° D.40°
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一道数学题.不是很难的.(1)如图,在△ABC中,∠ACB=100°,AC=AE,BC=BD,则∠DEC的度数为( )A.20° B.25° C.30° D.40°
一道数学题.不是很难的.
(1)如图,在△ABC中,∠ACB=100°,AC=AE,BC=BD,则∠DEC的度数为( )
A.20° B.25° C.30° D.40°

一道数学题.不是很难的.(1)如图,在△ABC中,∠ACB=100°,AC=AE,BC=BD,则∠DEC的度数为( )A.20° B.25° C.30° D.40°
∵AC=AE,BC=BD
∴∠ACE=∠AEC,∠BCD=∠BDC(等腰直角三角形的两底角相等且都等于45°)
∵∠ACB=100°
∴∠ACE+∠BCD=∠AEC+∠BDC=100°+∠DCE ①
∵在△DCE中,由三角形内角和定理有
∴∠AEC+∠BDC+∠DCE=180° ②
将①代入②,得
∴100°+∠DCE+∠DCE=180°
解得∠DCE=40°

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