a: \(\widehat{O_3}+\widehat{O_2}=180^0\)
=>\(2\cdot\widehat{O_2}+\widehat{O_2}=180^0\)
=>\(3\cdot\widehat{O_2}=180^0\)
=>\(\widehat{O_2}=\dfrac{180^0}{3}=60^0\)
\(\widehat{O_3}=2\cdot\widehat{O_2}=120^0\)
Ta có: \(\widehat{O_4}=\widehat{O_2}\)(hai góc đối đỉnh)
mà \(\widehat{O_2}=60^0\)
nên \(\widehat{O_4}=60^0\)
\(\widehat{O_1}=\widehat{O_3}\)(hai góc đối đỉnh)
mà \(\widehat{O_3}=120^0\)
nên \(\widehat{O_1}=120^0\)
b: Ta có: \(\widehat{O_1}-\widehat{O_2}=100^0\)
mà \(\widehat{O_1}+\widehat{O_2}=180^0\)
nên \(\widehat{O_1}=\dfrac{180^0+100^0}{2}=\dfrac{280^0}{2}=140^0\)
Ta có: \(\widehat{O_1}=\widehat{O_3}\)(hai góc đối đỉnh)
mà \(\widehat{O_1}=140^0\)
nên \(\widehat{O_3}=140^0\)
Có : \(\widehat{O2}+\widehat{O3}=180^0\)(kề bù)
Mà \(\widehat{2O2}=\widehat{O3}\)
`=>`\(\widehat{O2}+\widehat{2O2}=180^0\)
`=>`\(\widehat{3O2}=180^0\)
`=>`\(\widehat{O2}=180^0:3=60^0\)
`=>`\(\widehat{O3}=\widehat{2O2}=2.60^0=120^0\)
Lại có :\(\left[{}\begin{matrix}\widehat{O2}=\widehat{O4}=60^0\\\widehat{O1}=\widehat{O3}=120^0\end{matrix}\right.\)(đối dỉnh)
`b)`Có \(\widehat{O1}+\widehat{O2}=180^0\)(kề bù)
Mà \(\widehat{O1}-\widehat{O2}=100^0\)
`=>`\(\widehat{O1}=\left(180^0+100^0\right):2=140^0\)
Lại có :\(\widehat{O1}=\widehat{O3}=140^0\)(đói đỉnh)
