Which statement expresses the Linear Pair Postulate?

Which statement expresses the Linear Pair Postulate?

• A. Two angles forming a linear pair are perpendicular.
• B. Two angles forming a linear pair have equal measures.
• C. Two angles forming a linear pair have non-common sides equal.
• D. If two angles form a linear pair, they are supplementary.

Answer: (D)

The key idea being tested is that a linear pair consists of two adjacent angles whose non-common sides form a straight line, so together they fill a straight angle. This means their measures add up to 180 degrees, which is what it means to be supplementary. Therefore, the statement that two angles forming a linear pair are supplementary expresses the postulate exactly. You can picture a straight line with a vertex on it and two adjacent angles sharing that vertex; no matter how they split the line, the two angles together cover the whole straight angle, totaling 180 degrees. For example, if one angle is 120 degrees, the other must be 60 degrees. The ideas that they are perpendicular, that they have equal measures, or that their non-common sides are equal do not define the linear pair, so they don’t match the postulate.

The key idea being tested is that a linear pair consists of two adjacent angles whose non-common sides form a straight line, so together they fill a straight angle. This means their measures add up to 180 degrees, which is what it means to be supplementary. Therefore, the statement that two angles forming a linear pair are supplementary expresses the postulate exactly. You can picture a straight line with a vertex on it and two adjacent angles sharing that vertex; no matter how they split the line, the two angles together cover the whole straight angle, totaling 180 degrees. For example, if one angle is 120 degrees, the other must be 60 degrees. The ideas that they are perpendicular, that they have equal measures, or that their non-common sides are equal do not define the linear pair, so they don’t match the postulate.