Question

given nl is an angle bisector of ∠hnj, which conjecture must be true?

Explanation:

Step1: Recall angle - bisector definition

An angle bisector divides an angle into two congruent angles. Since \(NL\) is the angle - bisector of \(\angle HNJ\), we have \(\angle HNL=\angle JNL\).

Step2: Analyze the options

We know that by the definition of an angle bisector, if \(NL\) bisects \(\angle HNJ\), then the two angles formed by the bisector and the sides of the original angle are congruent. That is, \(\angle LNK\) and \(\angle KNJ\) are the two angles formed when \(NK\) is considered within \(\angle LNJ\) (and \(NL\) is the bisector of \(\angle HNJ\)). The correct conjecture is that the two angles formed by a ray within the bisected - angle region are congruent. So \(\angle LNK\cong\angle KNJ\).

Answer:

\(\angle LNK\cong\angle KNJ\)