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Giải bài 3 trang 115 SGK Toán 8 tập 1 - Cánh diều

Cho hình thoi ABCD có

♐Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Cánh diều

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Đề bài

Cho hình thoi ABCD có \(\widehat {C{\rm{D}}B} = {40^o}\). Tính số đo mỗi góc của hình thoi ABCD.

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Lời giải chi tiết

Do ABCD là hình thoi nên DB là tia phân giác của \(\widehat {CDA}\) Mà: \(\widehat {CDB} = {40^0} \Rightarrow \widehat {CDA} = {2.40^0} = {80^0} \Rightarrow \widehat {CBA} = \widehat {CDA} = {80^0}\) Mặt khác: \(\begin{array}{l}\widehat {BAD} + \widehat {CBA} + \widehat {CDA} + \widehat {BCD} = {360^0}\\\widehat {BAD} + {80^0} + {80^0} + \widehat {BCD} = {360^0}\end{array}\) (do ABCD là hình thoi nên \(\widehat {BAD} = \widehat {BCD}\)) \( \Rightarrow \widehat {BAD} = \widehat {BCD} = \frac{{{{360}^0} - {{80}^0} - {{80}^0}}}{2} = {100^0}\) Vậy hình thoi ABCD có: \(\widehat {BCA} = \widehat {CDA} = {80^0};\widehat {BAD} = \widehat {BCD} = {100^0}\)

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