Question

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

Answer 1

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}`