等腰梯形ABCD中,AD∥BC,AD＝DC＝AB,BD＝BC,求∠A的度数

题目

等腰梯形ABCD中,AD∥BC,AD＝DC＝AB,BD＝BC,求∠A的度数

答案

∵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°∴...