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歡迎您訪問數學考題練習:如圖,在矩形ABCD中,BC=2CD,∠EBC!

數學考題練習:如圖,在矩形ABCD中,BC=2CD,∠EBC

更新時間:2024-01-12 16:24:45作者:貝語網校

如圖,在矩形ABCD中,BC=2CD,∠EBC=30°,則∠DCE=________度.

試題答案

15

試題解析

利用矩形對邊平行的性質得到∠AEB=∠EBC=30°,進而求得∠ABE的度數.那么可得到BE=2AB,根據BC=2CD,可得到BC=BE,所以∠BEC=∠BCE,可得到∠BCE的度數,進而求得所求的角的度數.

解答:∵在矩形ABCD中.

∴AD=BC,AB=CD,AD∥BC,∠A=∠DCB=90°.

∴∠AEB=∠EBC=30°.

∴BE=2AB.

∵BC=2CD.

∴BC=BE.

∴∠BEC=∠BCE=75°.

∴∠DCE=15°.

點評:此題考查了矩形和直角三角形的性質,還考查了等腰三角形的性質,等邊對等角;解題的關鍵是要注意數形結合.

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