Given each definition or theorem, complete each statement. Supplement Theorem: If ZX and LY form a linear pair, then 2X +2Y are supplementary 2X + ZY are complementary m2X = m_Y
The Correct Answer and Explanation is:
Corrected Statement:
If angles ∠ZX and ∠LY form a linear pair, then they are supplementary; that is, their measures add up to 180°.
Explanation:
In geometry, a linear pair consists of two adjacent angles whose non-common sides form a straight line. This configuration implies that the two angles are supplementary, meaning their measures sum to 180°. This relationship is formalized in the Linear Pair Theorem, which states: If two angles form a linear pair, then they are supplementary.
For instance, if angle ∠ZX measures 110°, then angle ∠LY must measure 70°, since 110° + 70° = 180°. This ensures the two angles together form a straight angle.
It’s important to note that while all linear pairs are supplementary, not all supplementary angles form a linear pair. Supplementary angles can be non-adjacent and located in different parts of a diagram.
Regarding complementary angles, these are two angles whose measures sum to 90°. Complementary angles often appear in right-angled triangles, where the two non-right angles are complementary. However, in the context of linear pairs, the angles are supplementary, not complementary.
In summary, when two angles form a linear pair, they are adjacent and their non-common sides form a straight line, making them supplementary with a combined measure of 180°.