Explanation of "External Angle"
Definition:
An "external angle" is the angle formed outside a polygon when one side of the polygon is extended. It is the supplement (or complement) of an interior angle of that polygon. This means that if you add the external angle and the interior angle together, they equal 180 degrees.
Usage Instructions:
You can use "external angle" when discussing geometry, especially when talking about shapes like triangles, quadrilaterals, and other polygons.
It's important to understand that the external angle is related to the interior angle, so knowing one can help you find the other.
Example:
In a triangle, if one of the interior angles is 60 degrees, the external angle at that vertex would be 120 degrees because 180 - 60 = 120.
In a square, each interior angle is 90 degrees; therefore, each external angle is also 90 degrees because 180 - 90 = 90.
Advanced Usage:
In more advanced mathematics, you might encounter the concept of "external angles" in the context of the "external angle theorem," which states that the measure of an external angle is equal to the sum of the measures of the two opposite interior angles.
Word Variants:
External (adjective): Pertaining to the outside or outer part. For example, "external forces."
Angle (noun): A figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
Different Meanings:
External can refer to anything outside or outer, such as the external part of a building or the external factors affecting a situation.
Angle can also refer to a way of considering or presenting a situation, such as "looking at the problem from a different angle."
Synonyms:
For "external," you might use "outer," "outside," or "exterior."
For "angle," synonyms include "corner," "intersection," or "perspective" (in a figurative sense).
Idioms and Phrasal Verbs:
While there aren’t specific idioms or phrasal verbs directly related to "external angle," you might encounter phrases like: - "From another angle" - meaning to look at a situation from a different perspective. - "At an angle" - meaning something is not straight or aligned; it could refer to physical angles or metaphorically to attitudes or viewpoints.
Summary:
In summary, an "external angle" is an important concept in geometry that helps us understand the relationship between angles in polygons.