Bài 1
Vì a ⊥ c
b ⊥ c
\(\Rightarrow\) a // b
\(\Rightarrow\widehat{F}+\widehat{E}=180^0\) (trong cùng phía)
\(\Rightarrow x+y=180\)
\(\dfrac{x}{5}=\dfrac{y}{4}=\dfrac{x+y}{5+4}=\dfrac{180}{9}=20\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{x}{5}=20\\\dfrac{y}{4}=20\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=20.5=100\\y=20.4=80\end{matrix}\right.\)
Bài 2
Vẽ tia Oz nằm trong \(\widehat{AOB}\) sao cho Ax // Oz // By
Ax // Oz
\(\Rightarrow\widehat{xAO}=\widehat{AOz}\) ( so le trong )
mà \(\widehat{xAO}=32^0\)
\(\Rightarrow\widehat{AOz}=32^0\)
Vì Oz // By
\(\Rightarrow\widehat{zOB}+\widehat{OBy}=180^0\)
mà \(\widehat{OBy}=122^0\)
\(\Rightarrow\widehat{zOB}=58^0\)
Vì tia Oz nằm trong \(\widehat{AOB}\)
\(\Rightarrow\widehat{AOz}+\widehat{zOB}=\widehat{AOB}\)
Thay số : \(58^0+32^0=\widehat{AOB}\)
\(\Rightarrow\widehat{AOB}=90^0\)
\(\Rightarrow\) OA ⊥ OB
