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Giải bài 3 trang 111 SGK Toán 8 tập 1 - Cánh diều

Cho hình chữ nhật ABCD

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

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

෴Cho hình chữ nhật ABCD có điểm E nằm trên cạnh CD sao cho \(\widehat {A{\rm{E}}B} = {78^o};\widehat {EBC} = {39^o}\). Tính số đo của \(\widehat {BEC}\) và \(\widehat {E{\rm{A}}B}\).

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

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Lời giải chi tiết

Xét tam giác BEC vuông tại C có:

⭕\(\begin{array}{l}\widehat {BEC} + \widehat {EBC} + \widehat {BCE} = {180^o}\\ \Rightarrow \widehat {BEC} + {39^o} + {30^o} = {180^o}\\ \Rightarrow \widehat {BEC} = {180^o} - {39^o} - {30^o} = {51^o}\end{array}\)

Mà: \(\widehat {EBA} + \widehat {EBC} = {90^o}\)

🦋nên \(\widehat {EBA} = {90^o} - \widehat {EBC} = {90^o} - {39^o} = {51^o}\)

Xét tam giác AEB có:

ܫ\(\widehat {A{\rm{E}}B} + \widehat {E{\rm{A}}B} + \widehat {EBA} = {180^o}\)

🀅Suy ra \(\widehat {E{\rm{A}}B} = {180^o} - \widehat {A{\rm{E}}B} - \widehat {EBA}\) \( = {180^o} - {78^o} - {51^o} = {51^o}\)

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