Ta có:
\(\widehat{C_1}+\widehat{D_1}=180^0\) (vì 2 góc trong cùng phía) (1)
\(\widehat{C_1}-\widehat{D_1}=30^0\left(gt\right)\) (2)
Cộng (1) với (2) ta được:
\(\left(\widehat{C_1}+\widehat{D_1}\right)+\left(\widehat{C_1}-\widehat{D_1}\right)=180^0+30^0\)
=> \(\left(\widehat{C_1}+\widehat{D_1}\right)+\left(\widehat{C_1}-\widehat{D_1}\right)=210^0\)
=> \(2\widehat{C_1}=210^0\)
=> \(\widehat{C_1}=210^0:2\)
=> \(\widehat{C_1}=105^0.\)
=> \(105^0+\widehat{D_1}=180^0\)
=> \(\widehat{D_1}=180^0-105^0\)
=> \(\widehat{D_1}=75^0.\)
Vì \(a\) // \(b\left(gt\right)\)
=> \(\widehat{D_1}=\widehat{C_2}\) (vì 2 góc so le trong)
Mà \(\widehat{D_1}=75^0\left(cmt\right)\)
=> \(\widehat{C_2}=75^0.\)
Vì \(a\) // \(b\left(gt\right)\)
=> \(\widehat{C_1}=\widehat{D_2}\) (vì 2 góc so le trong)
Mà \(\widehat{C_1}=105^0\left(gt\right)\)
=> \(\widehat{D_2}=105^0.\)
Vậy.......
Chúc bạn học tốt!
