Answer: The value of x =8.
Step-by-step explanation:
We know that the incenter of triangle is constructed by taking the intersection of the angle bisectors of the three vertices of the triangle.
Thus if G is the incenter of [tex]\triangle DEF[/tex] then, it is bisecting [tex]\angle{F}[/tex]
[tex]\Rightarrow\angle{GFE}=\angle{GFD}[/tex]
[tex]\\\Rightarrow2x=16\\\Rightarrow\ x=8[/tex]
Therefore, the value of x=8.
