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Giải bài tập 7.14 trang 38 SGK Toán 9 tập 2 - Cùng khám phá

Tính số đo các góc của tứ giác nội tiếp ABCD trong Hình 7.23.

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

Toán - Văn - Anh
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Đề bài

Tính số đo các góc của tứ giác nội tiếp ABCD trong Hình 7.23.

Phương pháp giải - Xem chi tiết

♍Góc nội tiếp bằng nửa góc ở tâm cùng chắn một cung

൲Trong một tứ giác nội tiếp, tổng số đo hai góc đối nhau bằng \({180^o}\).

Lời giải chi tiết

🌱Ta có \(\widehat {ADC} = \frac{1}{2}\widehat {AOC} = \frac{1}{2}.\left( {{{65}^o} + {{78}^o}} \right) = 71,{5^o}\) (góc nội tiếp bằng nửa góc ở tâm cùng chắn cung AC)

🌺Suy ra \(\widehat {ABC} = {180^o} - \widehat {ADC} = {180^o} - 71,{5^o} = 108,{5^o}\)

𓄧\(\widehat {BCD} = \frac{1}{2}\widehat {BOD} = \frac{1}{2}.\left( {{{65}^o} + {{106}^o}} \right) = 85,{5^o}\)🐎(góc nội tiếp bằng nửa góc ở tâm cùng chắn cung BD)

𒉰Suy ra \(\widehat {BAD} = {180^o} - \widehat {BCD} = {180^o} - 85,{5^o} = 94,{5^o}\).

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