Có: a // b
\(\Rightarrow\widehat{C_1}+\widehat{D_1}=180^o\) (2 góc trong cùng phía) (1)
Mà \(\widehat{C_1}-\widehat{D_1}=50^o\Rightarrow\widehat{C_1}=50^o+\widehat{D_1}\)
Thay vào (1) ta có:
\(50^o+\widehat{D_1}+\widehat{D_1}=180^o\\ \Rightarrow2\widehat{D_1}=130^o\\ \Rightarrow\widehat{D_1}=65^o\)
\(\Rightarrow\widehat{C_1}=50^o+65^o=115^o\)
Có: \(\left\{{}\begin{matrix}\widehat{C_1}+\widehat{C_2}=180^o\\\widehat{D_1}+\widehat{D_2}=180^o\end{matrix}\right.\)(2 góc kề bù)
Thay số: \(\left\{{}\begin{matrix}115^o+\widehat{C_2}=180^o\\65^o+\widehat{D_2}=180^o\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}\widehat{C_2}=65^o\\\widehat{D_2}=115^o\end{matrix}\right.\)
Ta có:
\(\widehat{C_1}+\widehat{D_1}=180^0\) (vì 2 góc trong cùng phía) (1)
\(\widehat{C_1}-\widehat{D_1}=50^0\left(gt\right)\) (2)
Cộng (1) và (2) ta được:
\(\left(\widehat{C_1}+\widehat{D_1}\right)+\left(\widehat{C_1}-\widehat{D_1}\right)=180^0+50^0\)
=> \(\left(\widehat{C_1}+\widehat{D_1}\right)+\left(\widehat{C_1}-\widehat{D_1}\right)=230^0.\)
=> \(2.\widehat{C_1}=230^0\)
=> \(\widehat{C_1}=230^0:2\)
=> \(\widehat{C_1}=115^0.\)
=> \(115^0+\widehat{D_1}=180^0\)
=> \(\widehat{D_1}=180^0-115^0\)
=> \(\widehat{D_1}=65^0.\)
Vì \(a\) // \(b\left(gt\right)\)
=> \(\widehat{C_1}=\widehat{D_2}\) (vì 2 góc so le trong)
Mà \(\widehat{C_1}=115^0\left(cmt\right)\)
=> \(\widehat{D_2}=115^0.\)
Vì \(a\) // \(b\left(gt\right)\)
=> \(\widehat{D_1}=\widehat{C_2}\) (vì 2 góc so le trong)
Mà \(\widehat{D_1}=65^0\left(cmt\right)\)
=> \(\widehat{C_2}=65^0.\)
Vậy \(\widehat{D_2}=115^0;\widehat{C_2}=65^0.\)
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