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Giải bài 4.10 trang 69 SGK Toán 7 tập 1 - Kết nối tri thức

Cho tam giác ABC có BCA} = 60 và điểm M nằm trên cạnh BC sao cho

♌Tổng hợp đề thi học kì 2 lớp 7 tất cả các môn - Kết nối tri thức

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

Cho tam giác ABC có \(\widehat {BCA} = {60^o}\) và điểm M nằm trên cạnh BC sao cho \(\widehat {BAM} = {20^\circ },\widehat {AMC} = {80^\circ }({\rm{H}}.4.26).\) Tính số đo các góc AMB, ABC, BAC.

Phương pháp giải - Xem chi tiết

Áp dụng: + Tổng ba góc trong 1 tam giác bằng 180 độ + Tổng hai góc kề bù bằng 180 độ.

Lời giải chi tiết

Ta có:\(\widehat {AMB} + \widehat {AMC} = {180^o}\)( 2 góc kề bù)\(\begin{array}{l} \Rightarrow \widehat {AMB} + {80^o} = {180^o}\\ \Rightarrow \widehat {AMB} = {100^o}\end{array}\)Áp dụng định lí tổng ba góc trong một tam giác:+) Trong tam giác AMB có:\(\begin{array}{l}\widehat {ABC} + \widehat {MAB} + \widehat {AMB} = {180^O}\\ \Rightarrow \widehat {ABC} + {20^o} + {100^o} = {180^O}\\ \Rightarrow \widehat {ABC} = {60^o}\end{array}\)

+) Trong tam giác ABC có:
♓ \(\begin{array}{l}\widehat {BAC} + \widehat {ACB} + \widehat {CBA} = {180^o}\\ \Rightarrow \widehat {BAC} + {60^o} + {60^o} = {180^o}\\ \Rightarrow \widehat {BAC} = {60^o}\end{array}\)

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