如图,在△ABC中,AB=AC,BC=BD=ED=EA,求∠A的度数=_.
问题描述:
如图,在△ABC中,AB=AC,BC=BD=ED=EA,求∠A的度数=______.
答
∵AE=ED,∴∠ADE=∠A,∴∠DEB=∠A+∠ADE=2∠A,∵BD=ED,∴∠ABD=∠DEB=2∠A,∴∠BDC=∠A+∠ABD=3∠A,∵BD=BC,∴∠C=∠BDC=3∠A,∵AB=AC,∴∠ABC=∠C=3∠A,∵∠ABC+∠C+∠A=180°,∴7∠A=180°,∴∠A=180...