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Angle DGC measures 76 degrees. (a) What is the measure of Angle AGC? (b) What is the measure of Angle BGC?

Angle DGC measures 76 degrees. (a) What is the measure of Angle AGC? (b) What is the-example-1
User Jason Cook
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A.

We know that angles DGC and AGC are a linear pair. Therefore,


m\angle AGC+m\angle DGC=180

Since we already know the measurement of angle DGC,


\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}

B.

We know that angles DGC and BGC are complementary. This way,


m\angle BGC+m\angle AGC=90

Since we already know the measurement of angle DGC,


\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}

User Bram Stoker
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