Step 1 :Identify the angles formed by intersecting lines using the given information about parallel lines: \(\overleftrightarrow{G I}\) and \(\overleftrightarrow{J L}\)
Step 2 :Find the vertical angles, which are opposite to each other when two lines intersect
Step 3 :\(\boxed{\angle L K H \text{ and } \angle J K H \text{ are vertical angles}}\)