TL;DR – “Complementary” refers to two angles adding up to 90 degrees or things that complete each other, while “supplementary” pertains to two angles summing to 180 degrees or something added to enhance or complete an existing entity.
“Complementary” and “supplementary” are terms rooted in mathematics, particularly in geometry, but they also hold significance outside this realm in the English language:
Definition: In geometry, when two angles add up to a right angle, or 90 degrees, they are termed complementary angles. For instance, if you have an angle measure of 30 degrees, its complement would be 60 degrees. Outside of geometry, it means something that completes or goes well with something.
Usage: Beyond geometry, it often describes two or more things that enhance or emphasize the qualities of each other when combined.
Example: The wine and cheese were complementary, each enhancing the flavor of the other.
Definition: In geometry, when two angles combine to form a straight angle or 180 degrees, they are termed supplementary angles. If a given angle measures 120 degrees, its supplement is 60 degrees. Beyond geometry, it describes something added to complete or enhance a pre-existing item or concept.
Usage: Outside of angles, it generally refers to providing additional support or completion to an existing entity.
Example: The teacher offered supplementary materials to help students grasp the topic more profoundly.
In geometry, complementary angles share a vertex and are adjacent angles. The main difference from supplementary angles is that their measures add up to 90 degrees. This concept has its origins in the Latin word “complementum,” emphasizing the idea of completion.
In geometry, two angles that sum up to 180 degrees, such as a linear pair of angles, are supplementary. The term highlights the idea of “adding to” or “completing to 180 degrees.” Two angles being supplementary doesn’t necessarily mean they’re adjacent, but if they are on a straight line and share a vertex, they are supplementary.
Both complementary and supplementary angles play a role in algebra, graphing, and trigonometry. They’re foundational in theorems dealing with parallel lines cut by a transversal, and understanding these angles assists in solving for missing angles or applying concepts like congruent and vertical angles.
In summary, “complementary” and “supplementary” have precise definitions in geometry dealing with types of angles. However, in general English usage, “complementary” denotes items or ideas that are different but harmoniously paired, while “supplementary” indicates additions that complete or improve what’s already present. Understanding the nuanced differences between these terms aids in both mathematical and everyday contexts.
What is an example of a complementary and supplementary angle?
Let’s break this down:
- Definition: Two angles are complementary if the sum of their measures is 90°.
- Example: If one angle measures 35°, its complementary angle would be 90°−35°=55° because 35°+55°=90°.
- Definition: Two angles are supplementary if the sum of their measures is 180°.
- Example: If one angle measures 110°, its supplementary angle would be 180°−110°=70° because 110°+70°=180°.
In both examples, the two angles together either form a right angle (in the case of complementary angles) or a straight angle (in the case of supplementary angles).
Published on: 2023-10-03
Updated on: 2023-10-06