Question 355186
<pre>
{{{drawing(400,400,-1,1,-1,1,

line(-cos(34*pi/180),sin(34*pi/180),cos(34*pi/180),-sin(34*pi/180)),

line(-cos(34*pi/180),-sin(34*pi/180),cos(34*pi/180),sin(34*pi/180)), 
red(arc(0,0,.8,-.8,146,214)), red(arc(0,0,.8,-.8,326,394)),
locate(-cos(34*pi/180),sin(34*pi/180)-.03,K), locate(-cos(34*pi/180),-sin(34*pi/180),L),locate(cos(34*pi/180),sin(34*pi/180),J), locate(0-.03,0-.03,N),
locate(cos(34*pi/180),-sin(34*pi/180),M), locate(-.35,.03,10y-12),
locate(.1,.03,8y+4)
)}}}

Angles KNL and JNM are vertical angles so they are equal so

     10y - 12 = 8y + 4
           2y = 16
            y = 8

So angle KNL = 10y - 12 = 10(8) - 12 = 80 - 12 = 68°

and, as a check

Angle JNM = 8y + 4 = 8(8) + 4 = 64 + 4 = 68°

-----------------

So now we have  

{{{drawing(400,400,-1,1,-1,1,

line(-cos(34*pi/180),sin(34*pi/180),cos(34*pi/180),-sin(34*pi/180)),

line(-cos(34*pi/180),-sin(34*pi/180),cos(34*pi/180),sin(34*pi/180)), 
red(arc(0,0,.8,-.8,146,214)), 
locate(-cos(34*pi/180),sin(34*pi/180)-.03,K), locate(-cos(34*pi/180),-sin(34*pi/180),L),locate(cos(34*pi/180),sin(34*pi/180),J), locate(0-.03,0-.03,N),
locate(cos(34*pi/180),-sin(34*pi/180),M), locate(-.25,.03,"68°"),
green(arc(0,0,.8,-.8,34,146),locate(0,.3,"?"))
)}}}

and we want to find the angle JNK indicated by the green arc.

Angle KNL and angle JNK are supplementary, so 

Angle JNK  = 180° - Angle KNL

So

Angle JNK = 180° - 68° = 112°

{{{drawing(400,400,-1,1,-1,1,

line(-cos(34*pi/180),sin(34*pi/180),cos(34*pi/180),-sin(34*pi/180)),

line(-cos(34*pi/180),-sin(34*pi/180),cos(34*pi/180),sin(34*pi/180)), 
red(arc(0,0,.8,-.8,146,214)), 
locate(-cos(34*pi/180),sin(34*pi/180)-.03,K), locate(-cos(34*pi/180),-sin(34*pi/180),L),locate(cos(34*pi/180),sin(34*pi/180),J), locate(0-.03,0-.03,N),
locate(cos(34*pi/180),-sin(34*pi/180),M), locate(-.25,.03,"68°"),
green(arc(0,0,.8,-.8,34,146),locate(-.1,.3,"112°"))
)}}}

Edwin</pre>