解：∵ED＝EA∴∠AED＝∠A∴∠BED＝∠A+∠AED＝2∠A∵BD＝ED∴∠ABD＝∠BED＝2∠A∴∠BDC＝∠A+∠ABD＝3∠A∵BD＝BC∴∠C＝∠BDC＝3∠A∵AB＝AC∴∠ABC＝∠C＝3∠A∵∠A+∠ABC+∠C＝180∴8∠A＝180∴∠A＝22.5°
