We are given that lines HJ and KM are parallel. We notice that the angles:
[tex]\begin{gathered} \angle KLN \\ \angle HIL \end{gathered}[/tex]
Are corresponding angles, and therefore they are congruent, that is:
[tex]\angle KLN\cong\angle HIL[/tex]
Also, angles:
[tex]\begin{gathered} \angle HIL \\ \angle JIG \end{gathered}[/tex]
Are vertical angles, therefore, they are equal:
[tex]\angle HIL\cong\angle JIG[/tex]
Therefore, combining the two statements we get:
[tex]\angle KLN\cong\angle JIG[/tex]
Therefore:
[tex]\angle KLN=43[/tex]
Angle KLN equals 43 degrees.
