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Giải bài 3.7 trang 34 sách bài tập toán 8 - Kết nối tri thức với cuộc sống

Tính các góc của hình thang ABCD (AB,CD là hai đáy) biết (widehat A = 2widehat D), (widehat B = widehat C + 40^circ ).

🌠Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Khoa học tự nhiên
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Đề bài

Tính các góc của hình thang ABCD (AB,CD là hai đáy) biết \(\widehat A = 2\widehat D\), \(\widehat B = \widehat C + 40^\circ \).

Phương pháp giải - Xem chi tiết

Sử dụng tính chất của hình thang cân và áp dụng định lí tổng các góc trong một tứ giác.

Lời giải chi tiết

Trong hình thang ABCD có: \(\widehat A\) và \(\widehat D\) là hai góc bù nhau nên ta có \(\widehat A + \widehat D = 180^\circ \).Mà \(\widehat A = 2\widehat D\) nên \(2\widehat D + \widehat D = 180^\circ \), suy ra \(\widehat D = 60^\circ \).Do đó \(\widehat A = 2\widehat D = 2.60^\circ  = 120^\circ \).Tương tự \(\widehat B\) và \(\widehat C\) là hai góc bù nhau nên ta có \(\widehat B + \widehat C = 180^\circ \).Mà \(\widehat B = \widehat C + 40^\circ \) nên \(\widehat C + 40^\circ  + \widehat C = 180^\circ \) hay \(2\widehat C = 140^\circ \), suy ra \(\widehat C = 70^\circ \).Do đó \(\widehat B = \widehat C + 40^\circ  = 70^\circ  + 40^\circ  = 110^\circ \).Vậy hình thang ABCD có \(\widehat A = 120^\circ \); \(\widehat B = 110^\circ \); \(\widehat C = 70^\circ \); \(\widehat D = 60^\circ \).

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