First, establish that the two triangles are similar.
< J is congruent to N from the marked congruent angles and L <--> L because of the congruent vertical angles. Those correspondences force K <-- >M.
Lengths of corresponding sides of similar triangles are in proportion.
Looking at the triangle correspondence Triangle JKL ~ Triangle NML, the extended proportion is as follows:
JK/NM = KL/ML = JL/NL.
That equation comes directly from the triangle correspondence. JK was first and second in the line-up for Triangle JKL so it corresponds to NM, first and second in the line-up for Triangle NML. Then, I chose second and third to second and third, and finally 3rd and lst to 3rd and lst.
Notice that I have not looked at the given lengths of any triangle sides because without the information above, I would not know how to set up the equations.
JK/NM = KL/ML = JL/NL
My next step is to fill in the known values in this extended proportion.
30 / (NM) = 9 / 24 = 24 / NL
Select two fractions where you know 3 of the four quantities.
30 / (NM) = 9 / 24
9 (MN) = 30* 24
MN = (30* 24) / 9
MN = 80 ---> Option B
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9 / 24 = 24 / NL
9 (NL) = 24*24
NL = (24*24) / 9
NL = 64 --> Option C
Note: When you work triangle similarity problems, it is *critical* to get the correspondence of the vertices FIRST. That gives you the corresponding sides in a proportion through which you can find the sides you seek. Do check my work to ensure that I correctly read the side lengths.