Question

point a is the incenter of △def. what is the value of n? 7 11 14 15 (3n - 6)° 27°

Explanation:

Step1: Recall in - center property

The in - center of a triangle is the point of intersection of the angle bisectors of the triangle. So, the angles formed by the angle bisectors are equal. Here, since point A is the in - center of $\triangle{DEF}$, the two angles at vertex D are equal. That is, $3n - 6=27$.

Step2: Solve the equation for n

Add 6 to both sides of the equation $3n - 6=27$. We get $3n=27 + 6$, so $3n=33$. Then divide both sides by 3: $n=\frac{33}{3}=11$.

Answer:

11