What is the relationship between the angles of a linear pair?

What is the relationship between the angles of a linear pair?

• A. They are complementary.
• B. They are supplementary.
• C. They are congruent.
• D. They are equal to 180 degrees.

Answer: (B)

The angles of a linear pair are always supplementary, meaning their measures add up to 180 degrees. A linear pair consists of two adjacent angles formed when two lines intersect. The key characteristic of these angles is that they share a common arm (the line that separates them) and the other two arms (the lines that form them) extend in opposite directions. Due to the straight line formed at the intersection of these two lines, one angle plus the other must equal a straight angle, which measures 180 degrees. Therefore, when you sum the measures of the two angles in a linear pair, the result is exactly 180 degrees, confirming their supplementary nature. Knowing that angles are described as complementary when they add up to 90 degrees, or as congruent when they are equal in measure, helps in understanding that these definitions do not apply to the angles in a linear pair. Thus, the correct relationship is that they are supplementary.

The angles of a linear pair are always supplementary, meaning their measures add up to 180 degrees. A linear pair consists of two adjacent angles formed when two lines intersect. The key characteristic of these angles is that they share a common arm (the line that separates them) and the other two arms (the lines that form them) extend in opposite directions.

Due to the straight line formed at the intersection of these two lines, one angle plus the other must equal a straight angle, which measures 180 degrees. Therefore, when you sum the measures of the two angles in a linear pair, the result is exactly 180 degrees, confirming their supplementary nature.

Knowing that angles are described as complementary when they add up to 90 degrees, or as congruent when they are equal in measure, helps in understanding that these definitions do not apply to the angles in a linear pair. Thus, the correct relationship is that they are supplementary.