In the figure, angle LNM = 40 degrees
How to find angle LNM
According to the figure, angle LNM and angle LKJ are corresponding angles.
Also, the figure shows that correponding angles are congruent. Hence we have the equation
-16 + 8x = -23 + 9x
-16 + 23 = 9x - 8x
x = 7
Then, angle LNM = -23 + 9x
angle LNM = -23 + 9 * 7
angle LNM = 40 degrees