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______.
答
∵DE是AB的垂直平分线,
∴AE=BE,
∴∠ABE=∠A=36°,
∵AB=AC,
∴∠ABC=∠C=
=72°,180°−∠A 2
∴∠EBC=∠ABC-∠ABE=72°-36°=36°.
故答案为:36°.