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Question

Cho 2 đường thẳng AB và CD cắt nhau tại I (I nằm giữa A và B,I nằm giữa C và D).Vẽ góc BIE=30 độ sao cho tia IB là tia phân giác của góc DIE.Tính số đo góc AIC và số đo góc CIE.

vũ hải đăng · Accepted Answer

Giải bài toán

Vì BIÊ=30∘modified cap B cap I cap E with hat above equals 30 raised to the composed with power𝐵𝐼𝐸=30∘và BIÊmodified cap B cap I cap E with hat above𝐵𝐼𝐸và DIÊmodified cap D cap I cap E with hat above𝐷𝐼𝐸là hai góc đối đỉnh, nên DIÊmodified cap D cap I cap E with hat above𝐷𝐼𝐸= 180−BIÊ180 minus modified cap B cap I cap E with hat above180−𝐵𝐼𝐸= 180−30=150180 minus 30 equals 150180−30=150 độ.
Vì tia IB là tia phân giác của góc DIE, nên DIÊ=CIÊ=30∘modified cap D cap I cap E with hat above equals modified cap C cap I cap E with hat above equals 30 raised to the composed with power𝐷𝐼𝐸=𝐶𝐼𝐸=30∘.
Vì BIÊmodified cap B cap I cap E with hat above𝐵𝐼𝐸và AIĈmodified cap A cap I cap C with hat above𝐴𝐼𝐶là hai góc đối đỉnh, nên AIĈmodified cap A cap I cap C with hat above𝐴𝐼𝐶= BIÊmodified cap B cap I cap E with hat above𝐵𝐼𝐸= 30∘30 raised to the composed with power30∘.
Vì BIÊmodified cap B cap I cap E with hat above𝐵𝐼𝐸và CIÊmodified cap C cap I cap E with hat above𝐶𝐼𝐸là hai góc kề bù, nên BIÊmodified cap B cap I cap E with hat above𝐵𝐼𝐸+ CIÊmodified cap C cap I cap E with hat above𝐶𝐼𝐸= 180∘180 raised to the composed with power180∘.
Từ đó, ta có BIÊmodified cap B cap I cap E with hat above𝐵𝐼𝐸+ CIÊmodified cap C cap I cap E with hat above𝐶𝐼𝐸= 180∘180 raised to the composed with power180∘ - 30∘30 raised to the composed with power30∘, nên CIÊmodified cap C cap I cap E with hat above𝐶𝐼𝐸= 150∘150 raised to the composed with power150∘.

Cách 2:

Vì BIÊmodified cap B cap I cap E with hat above𝐵𝐼𝐸và AIĈmodified cap A cap I cap C with hat above𝐴𝐼𝐶là hai góc đối đỉnh, nên AIĈmodified cap A cap I cap C with hat above𝐴𝐼𝐶= BIÊmodified cap B cap I cap E with hat above𝐵𝐼𝐸= 30∘30 raised to the composed with power30∘.
Vì BIÊmodified cap B cap I cap E with hat above𝐵𝐼𝐸và DIÊmodified cap D cap I cap E with hat above𝐷𝐼𝐸là hai góc kề bù, nên BIÊmodified cap B cap I cap E with hat above𝐵𝐼𝐸+ DIÊmodified cap D cap I cap E with hat above𝐷𝐼𝐸= 180∘180 raised to the composed with power180∘.
Từ đó, ta có 30∘30 raised to the composed with power30∘ + DIÊmodified cap D cap I cap E with hat above𝐷𝐼𝐸= 180∘180 raised to the composed with power180∘, nên DIÊmodified cap D cap I cap E with hat above𝐷𝐼𝐸= 150∘150 raised to the composed with power150∘.
Vì tia IB là tia phân giác của góc DIE, nên CIÊ=DIÊ2=1502=75∘modified cap C cap I cap E with hat above equals the fraction with numerator modified cap D cap I cap E with hat above and denominator 2 end-fraction equals 150 over 2 end-fraction equals 75 raised to the composed with power𝐶𝐼𝐸=𝐷𝐼𝐸2=1502=75∘.

Kết luận:

Số đo góc AIC là 150∘150 raised to the composed with power150∘ và CIE là 60∘60 raised to the composed with power60∘.

Câu trả lời: Giải bài toán

Vì BIÊ=30∘modified cap B cap I cap E with hat above equals 30 raised to the composed with power𝐵𝐼𝐸=30∘và BIÊmodified cap B cap I cap E with hat above𝐵𝐼𝐸và DIÊmodified cap D cap I cap E with hat above𝐷𝐼𝐸là hai góc đối đỉnh, nên DIÊmodified cap D cap I cap E with hat above𝐷𝐼𝐸= 180−BIÊ180 minus modified cap B cap I cap E with hat above180−𝐵𝐼𝐸= 180−30=150180 minus 30 equals 150180−30=150 độ.
Vì tia IB là tia phân giác của góc DIE, nên DIÊ=CIÊ=30∘modified cap D cap I cap E with hat above equals modified cap C cap I cap E with hat above equals 30 raised to the composed with power𝐷𝐼𝐸=𝐶𝐼𝐸=30∘.
Vì BIÊmodified cap B cap I cap E with hat above𝐵𝐼𝐸và AIĈmodified cap A cap I cap C with hat above𝐴𝐼𝐶là hai góc đối đỉnh, nên AIĈmodified cap A cap I cap C with hat above𝐴𝐼𝐶= BIÊmodified cap B cap I cap E with hat above𝐵𝐼𝐸= 30∘30 raised to the composed with power30∘.
Vì BIÊmodified cap B cap I cap E with hat above𝐵𝐼𝐸và CIÊmodified cap C cap I cap E with hat above𝐶𝐼𝐸là hai góc kề bù, nên BIÊmodified cap B cap I cap E with hat above𝐵𝐼𝐸+ CIÊmodified cap C cap I cap E with hat above𝐶𝐼𝐸= 180∘180 raised to the composed with power180∘.
Từ đó, ta có BIÊmodified cap B cap I cap E with hat above𝐵𝐼𝐸+ CIÊmodified cap C cap I cap E with hat above𝐶𝐼𝐸= 180∘180 raised to the composed with power180∘ - 30∘30 raised to the composed with power30∘, nên CIÊmodified cap C cap I cap E with hat above𝐶𝐼𝐸= 150∘150 raised to the composed with power150∘.

Cách 2:

Vì BIÊmodified cap B cap I cap E with hat above𝐵𝐼𝐸và AIĈmodified cap A cap I cap C with hat above𝐴𝐼𝐶là hai góc đối đỉnh, nên AIĈmodified cap A cap I cap C with hat above𝐴𝐼𝐶= BIÊmodified cap B cap I cap E with hat above𝐵𝐼𝐸= 30∘30 raised to the composed with power30∘.
Vì BIÊmodified cap B cap I cap E with hat above𝐵𝐼𝐸và DIÊmodified cap D cap I cap E with hat above𝐷𝐼𝐸là hai góc kề bù, nên BIÊmodified cap B cap I cap E with hat above𝐵𝐼𝐸+ DIÊmodified cap D cap I cap E with hat above𝐷𝐼𝐸= 180∘180 raised to the composed with power180∘.
Từ đó, ta có 30∘30 raised to the composed with power30∘ + DIÊmodified cap D cap I cap E with hat above𝐷𝐼𝐸= 180∘180 raised to the composed with power180∘, nên DIÊmodified cap D cap I cap E with hat above𝐷𝐼𝐸= 150∘150 raised to the composed with power150∘.
Vì tia IB là tia phân giác của góc DIE, nên CIÊ=DIÊ2=1502=75∘modified cap C cap I cap E with hat above equals the fraction with numerator modified cap D cap I cap E with hat above and denominator 2 end-fraction equals 150 over 2 end-fraction equals 75 raised to the composed with power𝐶𝐼𝐸=𝐷𝐼𝐸2=1502=75∘.

Kết luận:

Số đo góc AIC là 150∘150 raised to the composed with power150∘ và CIE là 60∘60 raised to the composed with power60∘.

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