Ta có: \(\widehat{A}+\widehat{B}=360^o-\left(\widehat{C}+\widehat{D}\right)=360^o-210^o=150^o\)

=> \(\widehat{A_1}+\widehat{B_1}=\dfrac{1}{2}\widehat{A}+\dfrac{1}{2}\widehat{B}=\dfrac{1}{2}\left(\widehat{A}+\widehat{B}\right)=\dfrac{150^o}{2}=75^o\)

=> \(\widehat{AIB}=180^o-\left(\widehat{A_1}+\widehat{B_1}\right)=180^o-75^o=105^o\)

2)Ta có: \(x^{3m+1}+x^{3n+2}+1\)= \(x^{3m+1}-x+x^{3n+2}-x^2+x^2+x+1\)

= \(x\left(x^{3m}-1\right)+x^2\left(x^{3n}-1\right)+\left(x^2+x+1\right)\)

Ta thấy: \(x^{3m}-1=\left(x^3\right)^m-1=\left(x^3-1\right)k\) \(⋮\) \(x^3-1\)

\(x^{3n}-1=\left(x^3\right)^n-1=\left(x^3-1\right)h\) \(⋮\) \(x^3-1\)

Do đó: \(x\left(x^{3m}-1\right)+x^2\left(x^{3n}-1\right)+\left(x^2+x+1\right)\) chia hết cho \(x^2+x+1\)

Vậy \(x^{3m+1}+x^{3n+2}+1\) chia hết cho \(x^2+x+1\)