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Giải bài tập 9.32 trang 91 SGK Toán 9 tập 2 - Kết nối tri thức

Cho tứ giác ABCD nội tiếp đường tròn (O), AB cắt CD tại E, AD cắt BC tại F như Hình 9.58. Biết (widehat {BEC} = {40^o}) và (widehat {DFC} = {20^o}), tính số đo các góc của tứ giác ABCD.

Tổng hợp Đề thi vào 10 có đáp án và lời giải

Toán - Văn - Anh
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Đề bài

Cho tứ giác ABCD nội tiếp đường tròn (O), AB cắt CD tại E, AD cắt BC tại F như Hình 9.58. Biết \(\widehat {BEC} = {40^o}\) và \(\widehat {DFC} = {20^o}\), tính số đo các góc của tứ giác ABCD.

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

+ Tính góc BCD, góc ADC, góc ABC theo góc A bằng cách sử dụng tính chất tứ giác nội tiếp và tổng các góc trong một tam giác. + Sử dụng kiến thức tổng các góc trong một tứ giác để tính góc A, từ đó tính được các góc còn lại.

Lời giải chi tiết

Vì tứ giác ABCD nội tiếp đường tròn (O) nên \(\widehat A + \widehat {BCD} = {180^o} \Rightarrow \widehat {BCD} = {180^o} - \widehat A\) Tam giác ADE có: \(\widehat {ADC} = {180^o} - \widehat E - \widehat A = {140^o} - \widehat A\) Tam giác ABF có: \(\widehat {ABC} = {180^o} - \widehat F - \widehat A = {160^o} - \widehat A\) Tứ giác ABCD có: \(\widehat A + \widehat {BCD} + \widehat {ABC} + \widehat {ADC} = {360^o}\) \( \Rightarrow \widehat A + {180^o} - \widehat A + {140^o} - \widehat A + {160^o} - \widehat A = {360^o}\) \( \Rightarrow {480^o} - 2\widehat A = {360^o} \Rightarrow \widehat A = {60^o}\) Do đó, \(\widehat {BCD} = {120^o},\widehat {ADC} = {80^o},\widehat {ABC} = {100^o}\)

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Tham Gia Group Dành Cho Lớp 9 - Ôn Thi Vào Lớp 10 Miễn Phí

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