A.
We know that angles DGC and AGC are a linear pair. Therefore,
[tex]m\angle AGC+m\angle DGC=180[/tex]
Since we already know the measurement of angle DGC,
[tex]\begin{gathered} m\angle AGC+m\angle DGC=180 \\ \rightarrow m\angle AGC+76=180 \\ \rightarrow m\angle AGC=180-76 \\ \\ \Rightarrow m\angle AGC=104 \end{gathered}[/tex]
B.
We know that angles DGC and BGC are complementary. This way,
[tex]m\angle BGC+m\angle AGC=90[/tex]
Since we already know the measurement of angle DGC,
[tex]\begin{gathered} m\angle BGC+m\angle AGC=90 \\ \rightarrow m\angle BGC+76=90 \\ \rightarrow m\angle BGC=90-76 \\ \\ \Rightarrow m\angle BGC=14 \end{gathered}[/tex]
