Question

given that point g is the in - center of △hjk, which of the following is true? m∠dhe=m∠kfg m∠jdg=m∠kfg two of these m∠djg=m∠fjg

Explanation:

Step1: Recall in - center property

The in - center of a triangle is the point of intersection of the angle bisectors of the triangle.

Step2: Analyze angle relationships

Since $G$ is the in - center of $\triangle HJK$, $JG$ is an angle bisector of $\angle HJK$. So, $m\angle DJG = m\angle FJG$.

Step3: Analyze other options

There is no information to suggest that $m\angle DHE=m\angle KFG$ or $m\angle JDG = m\angle KFG$. So the correct option is the one related to the angle - bisecting property of the in - center.

Answer:

D. $m\angle DJG = m\angle FJG$