The angle KLJ is 73°.
In the diagram, we see that ∠KJL and ∠KLJ are corresponding angles. Since the lines GH and JL are parallel, we know that corresponding angles are equal. Therefore, m∠KJL=m∠KLJ.
We can also see that △KJG∼△LJH by AA similarity. This means that the ratios of corresponding side lengths are equal. In particular, we have the following proportion:
JL / KJ = JH / JG
Substituting in the given values, we get:
9x−62 / 5x−2 = 5x−2 / 9x−62
Cross-multiplying and solving for x, we get x=13. Therefore, m∠KJL= m∠KLJ = 73°.