Question

Find the value of X and measure of angle GIF.

Answer 1

Applying linear pair property on the line DG,

`\begin{gathered} 8x+7+59^(\circ)+12x-6=180^(\circ) \\ \Rightarrow20x+60=180 \\ \Rightarrow20x=120 \\ \Rightarrow x=6 \end{gathered}`

The measure of angle GIF can be determined as,

`\begin{gathered} \angle GIF=12x-6 \\ =12*6-6 \\ =72-6 \\ =66^(\circ) \end{gathered}`

Thus, the required value of x is 6 and angle GIF is 66 degress.