In the diagram, KL ≅ NR and JL ≅ MR. What additional information is needed to show ΔJKL ≅ ΔMNR by SAS? ∠J ≅ ∠M ∠L ≅ ∠R ∠K ≅ ∠N ∠R ≅ ∠K

Did you ever figure the answer out?

According to SAS theorem which means Side Angle Side,

The angle which is included between the two sides must be congruent.

Here we are given that

KL = NR

JL = MR

Now in the figure we can clearly see that the angle included between JL & KL is L & the angle included between NR & MR is R.

So for the triangles to be congruent by SAS, angle L must be congruent to angle R.

∠L=∠R

Second option is the right answer.