Final answer:
Linear pairs consist of adjacent angles that add up to 180 degrees, and vertical angles formed by intersecting lines are congruent. Knowing one angle allows you to calculate the others using these properties.
Step-by-step explanation:
When two lines intersect, they create angles with specific relationships. The properties of linear pairs and vertical angles can help determine the angle measures created by the intersecting lines. A linear pair consists of two adjacent angles that are on the same line and add up to 180 degrees. On the other hand, vertical angles are the angles opposite each other when two lines intersect. These vertical angles are congruent, which means they have the same measure.
Therefore, the correct answer to how linear pairs and vertical angles help to determine the angle measures created by intersecting lines is: (b) Linear pairs determine the sum of two adjacent angles formed by intersecting lines, while vertical angles are equal in measure. This means that if you know one angle, you can find the measure of its linear pair by subtracting from 180 degrees, and if you know one vertical angle, you automatically know the measure of the angle opposite to it.