如图所示,在△ABC中,AB=AC,点D在BC上,且CA=CD,DA=DB,求△ABC各角的度数_数学解答

如图所示,在△ABC中,AB=AC,点D在BC上,且CA=CD,DA=DB,求△ABC各角的度数

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解答

∵CA＝CD,∴∠CAD＝∠CDA,∴∠ACB＝180°－2∠CDA.
∵DA＝DB,∴∠ABC＝∠BAD,∴∠CDA＝2∠ABC,∴2∠CDA＝4∠ABC.
∴∠ACB＝180°－4∠ABC.
∵AB＝AC,∴ACB＝∠ABC,∴∠ABC＝180°－4∠ABC,∴5∠ABC＝180°,∴∠ABC＝36°,
∴∠ACB＝36°,∴∠BAC＝180°－2∠ABC＝180°－2×36°＝108°.
即△ABC中∠A、∠B、∠C的度数依次是：108°、36°、36°.