Final answer:
Linear pairs of angles are supplementary, meaning they add up to 180 degrees, while vertical angles are congruent, meaning they have equal measures. These properties are essential in determining the angle measures formed by two intersecting lines.
Step-by-step explanation:
When two lines intersect, they form four angles. Understanding the properties of linear pairs and vertical angles is crucial in determining the measures of these angles.
A linear pair consists of two adjacent angles whose non-common sides are opposite rays. These angles add up to 180 degrees, making them supplementary. This property is particularly helpful in solving for unknown angle measures when one angle is given, as the other angle in the linear pair can be found by subtracting the given angle from 180 degrees.
Vertical angles, on the other hand, are the angles opposite each other when two lines intersect. They are called 'vertical' because they share the same vertex. A key property of vertical angles is that they are always congruent, meaning they have equal measures. If one vertical angle measures 50 degrees, the angle opposite to it will also measure 50 degrees. Knowing that vertical angles are equal allows us to solve for their measures when only one is known.
In conclusion, when dealing with intersecting lines, recognizing that linear pairs are supplementary (B) helps us understand they add up to 180 degrees, not 90 degrees as other options suggest. And recognizing that vertical angles are equal (D) clarifies that they are congruent, not supplementary or forming any other specific angle measure with each other.