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如图,在△ABC中,点D在AC上,且AB=AD,∠ABC=∠c+30°,则∠CBD的度数为?

来源:学生作业帮 编辑:拍题作业网作业帮 分类:综合作业 时间:2024/04/27 22:22:32
如图,在△ABC中,点D在AC上,且AB=AD,∠ABC=∠c+30°,则∠CBD的度数为?

AB=AD
∠ABD = ∠ADB
∠ABD + ∠ADB + ∠A = 180°
=> ∠ABD = (180°-∠A)/2
∠ABC = ∠C + 30°
∠ABC + ∠C + ∠A = 180°
∠ABC + (∠ABC - 30°) + ∠A = 180°
=> ∠ABC = (210°-∠A)/2
=> ∠CBD = ∠ABC - ∠ABD = 15°