Let [tex]\hat{G}, \hat{H}, \hat{I}[/tex] be the measures of the angles. We know that [tex]\hat{H} = \hat{G}+20[/tex] and [tex]\hat{G} = \hat{I}+8[/tex].
Moreover, we know that the sum of the interior angles of a triangle is 180:
[tex]\hat{H} + \hat{G}+\hat{I}=180[/tex]
So, we have the following system:
[tex]\begin{cases}\hat{H}=\hat{G}+20\\\hat{G}=\hat{I}+8\\\hat{G}+\hat{H}+\hat{I}=180\end{cases}[/tex]
Using the first two equations, we can express [tex]\hat{H}[/tex] and [tex]\hat{I}[/tex] in terms of [tex]\hat{G}[/tex]:
[tex]\hat{H}=\hat{G}+20,\quad \hat{I}=\hat{G}-8[/tex]
So, the last equation becomes
[tex]\hat{G}+(\hat{G}+20)+(\hat{G}-8)=180 \iff 3\hat{G}+12=180 \iff 3\hat{G}=168 \iff \hat{G}=56[/tex]
And we deduce
[tex]\hat{H}=\hat{G}+20=76,\quad \hat{I}=\hat{G}-8=48[/tex]
