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.

Explanation:

Step1: Vertical Angles

Vertical angles are equal. So, one of the unknown angles is \(51^{\circ}\) (opposite to the given \(51^{\circ}\) angle) and another is \(129^{\circ}\) (opposite to the given \(129^{\circ}\) angle).

Step2: Linear Pair

Angles on a straight line (linear pair) sum to \(180^{\circ}\). But since we already used the vertical - angle property (which is a result of the intersection of two lines and the angle - sum properties), we can confirm the measures.

Answer:

The three unknown angle measures are \(51^{\circ}\), \(129^{\circ}\), and \(129^{\circ}\) (if we consider the three non - given angles in the intersection, two of them are \(129^{\circ}\) and one is \(51^{\circ}\)).