Answer:
B. 11
Step-by-step explanation:
We have been given an image of a triangle and we are asked to find the value of n.
Since we know that in-center of a triangle is the point, where all the angle bisectors of a triangle meet.
Since we have been given that point A is the in-center of ΔDEF. This means the that DN is the angle bisector of angle EDF, so value of [tex](3n-6)^{\circ}[/tex] will be equal to [tex]27^{\circ}[/tex]
We can represent this information in an equation as:
[tex](3n-6)^{\circ}=27^{\circ}[/tex]
[tex]3n-6=27[/tex]
[tex]3n-6+6=27+6[/tex]
[tex]3n=33[/tex]
Let us divide both sides of our equation by 3.
[tex]\frac{3n}{3}=\frac{33}{3}[/tex]
[tex]n=11[/tex]
Therefore, the value of n is 11 and option B is the correct choice.
