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Giải Bài 42 trang 116 sách bài tập toán 7 tập 1 - Cánh diều

Tìm số đo góc QRS trong Hình 52, biết aa’ // cc’.

ᩚᩚᩚᩚᩚᩚ⁤⁤⁤⁤ᩚ⁤⁤⁤⁤ᩚ⁤⁤⁤⁤ᩚ𒀱ᩚᩚᩚTổng hợp đề thi học kì 2 lớp 7 tất cả các môn - Cánh diều

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Đề bài

Tìm số đo góc QRS trong Hình 52, biết aa’ // cc’.

Phương pháp giải - Xem chi tiết

Tính số đo góc QRS dựa vào số đo góc PRS. Muốn tính số đo góc PRS♏ ta dựa vào tính chất của hai đường thẳng song song.

Lời giải chi tiết

Ta có aa’ // cc’𒅌 nên \(\widehat {dQa'} = \widehat {aQd'} = 30^\circ \) (đối đỉnh).

Mà tổng của hai góc trong aQR và bRQ bằng 180°. Suy ra aa’ // bb’ // cc’.

Ta có aa’ // cc’ 🐻nên \(\widehat {dQa'} = \widehat {dPc'} = 30^\circ \) (hai góc đồng vị).

Mặt khác: hai góc RSc’ và RSP (RSc’)🐠 kề bù nhau nên \(\widehat {RSP} = 180^\circ  - 130^\circ  = 50^\circ \).

Xét tam giác RPS🍃 có tổng ba góc trong một tam giác bằng 180° nên \(\widehat {PRS} = 180^\circ  - 30^\circ  - 50^\circ  = 100^\circ \).

Mà hai góc PRS và QRS🍒 kề bù nhau nên \(\widehat {QRS} = 180^\circ  - \widehat {PRS} = 180^\circ  - 100^\circ  = 80^\circ \).

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