Question 1205619
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It's strange that point J is omitted as a label in this diagram.
I'll assume that point J is where the 161 degree angle is located.


The exterior angle 161 is adjacent to some interior angle x.
161+x = 180
x = 180-161
x = 19
Therefore angle NJK = 19 degrees.


Extend segment LN so that it intersects with JK.
Let's mark point P as the intersection of LN and JK.
This forms right triangle JPN.
Refer to the diagram below.
In the previous paragraph we found that angle J of triangle JPN is 19 degrees.
The other acute angle must be 90-19 = 71 degrees.
This is the measure of angle PNJ.


Angles PNJ and LNM are congruent vertical angles.
angle LNM = 71 and so is angle KNM due to the given info.


Focus on the angles: LNM, MNK, KNP
They glue together to form a straight line.
(angleLNM) + (angleMNK) + (angleKNP) = 180
(71) + (71) + (y) = 180
142+y = 180
y = 180-142
y = 38
angleKNP = 38 degrees


The last thing to focus on is right triangle PNK.
The conclusion of the last paragraph tells us that angle N = 38, so the other acute angle must be 90-38 = <font color=red>52 degrees which is the final answer</font>
*[illustration UploadedScreenshot_12.png]
I'll leave verification for the student to do.
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