Question

line jl and line khm 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 khm at point h, with angles 51°, 129°, 129° labeled, and points j, k, m, l marked)

Explanation:

Step1: Analyze Vertical Angles

Vertical angles are formed when two lines intersect. They are opposite each other and have equal measures. In the figure, angles on opposite sides of point \( H \) (vertical angles) like the \( 51^\circ \) angles and the \( 129^\circ \) angles are equal. Supplementary angles add up to \( 180^\circ \), but vertical angles are equal, not supplementary (unless they are \( 90^\circ \), which they aren't here).

Step2: Confirm the Correct Option

The first option says "They have the same measure," which matches the property of vertical angles. The second option says "They are supplementary," which is true for adjacent angles formed by intersecting lines (since \( 51^\circ + 129^\circ = 180^\circ \)), but not for opposite (vertical) angles. So the correct statement about angles on opposite sides of \( H \) is that they have the same measure.

Answer:

They have the same measure.