等腰梯形ABCD中,AD∥BC,AD＝DC＝AB,BD＝BC,求∠A的度数_数学解答

等腰梯形ABCD中,AD∥BC,AD＝DC＝AB,BD＝BC,求∠A的度数

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解答

∵等腰梯形ABCD∴∠ABC＝∠C∵AD＝AB∴∠ABD＝∠ADB∵AD//BC∴∠ADB＝∠CBD∴∠ABD＝∠CBD＝∠ABC/2∴∠ADB＝∠ABC/2∴∠ADB＝∠C/2∵BD＝BC∴∠BDC＝∠C∵AD//BC∴∠C+∠BDC+∠ADB＝180°∴∠C+∠C+∠C/2＝180°∴...