如图,在△ABC中,AB=AC,∠A=36°,AB的垂直平分线交AC于点E,垂足为点D,连接BE,则∠EBC的度数为_.

问题描述:

 如图,在△ABC中,AB=AC,∠A=36°,AB的垂直平分线交AC于点E,垂足为点D,连接BE,则∠EBC的度数为______.

∵DE是AB的垂直平分线,
∴AE=BE,
∴∠ABE=∠A=36°,
∵AB=AC,
∴∠ABC=∠C=

180°−∠A
2
=72°,
∴∠EBC=∠ABC-∠ABE=72°-36°=36°.
故答案为:36°.