imagine two lines intersect. how can the properties of linear pairs and vertical angles help to determine…

Explanation:

Step1: Recall linear - pair property

Linear pairs are adjacent angles formed by two intersecting lines. The sum of the measures of angles in a linear pair is 180°. If we know the measure of one angle in a linear pair, we can find the measure of the other by subtracting the known angle measure from 180°. For example, if one angle of a linear pair is (x), the other is (180 - x).

Step2: Recall vertical - angle property

Vertical angles are the non - adjacent angles formed by two intersecting lines. Vertical angles are congruent. So, if we find the measure of one angle formed by the intersecting lines, we can find the measure of its vertical - angle as they have the same measure.

Answer:

We can use the property that linear pairs of angles sum to 180° to find the measure of an adjacent angle when one is known. And we can use the property that vertical angles are congruent to find the measure of non - adjacent angles.