Question

line jl and line km intersect at point h. find the three unknown angle measures in the figure
what do you notice about the angles
on opposite sides of point h?
they have the same measure.
they are supplementary.
(image of intersecting lines jl and km at h, with angles 51°, 129°, 129°, 51° marked)

Explanation:

Looking at the intersecting lines at point H, the opposite (vertical) angles are $\angle JHK = 51^\circ$ and $\angle MHL = 51^\circ$, $\angle JHM = 129^\circ$ and $\angle KHL = 129^\circ$. These opposite angles have identical measures, which is the property of vertical angles. Supplementary angles add to $180^\circ$, which describes adjacent angles here, not opposite ones.

Answer:

They have the same measure.