Question

a
b
c
d

Explanation:

Step1: Analyze option A

There is no information given in the diagram to suggest that \(\overline{KL}\) and \(\overline{EF}\) are congruent.

Step2: Analyze option B

\(\angle LJK\) and \(\angle FJE\) are vertical angles. By the vertical - angles theorem, vertical angles are congruent. So \(\angle LJK\cong\angle FJE\).

Step3: Analyze option C

The diagram shows that \(EJ = LJ\) (marked with the same tick - mark), but there is no indication that \(JK\cong JE\).

Step4: Analyze option D

We know \(\angle LJK\cong\angle FJE\) from step 2. But there is no information in the diagram (such as parallel lines or other congruent parts) to suggest that \(\angle K\cong\angle E\).

Answer:

B. \(\angle LJK\cong\angle FJE\)