Definition

1. Noun:
   • The angle formed by one side of a polygon and the extension of an adjacent side: An external angle is the angle outside a polygon, created when a side is extended outward from a vertex. It is supplementary to the interior angle at that vertex.

Usage

• The term "external angle" is used in geometry to describe the angle outside a polygon. It is often discussed in relation to its corresponding interior angle, as the two angles always sum to 180 degrees (they are supplementary).
• Example: "To find the measure of an external angle, subtract the interior angle from 180 degrees."

Examples

• Noun:
  • The sum of the external angles of any convex polygon is always 360 degrees.
  • In a regular hexagon, each internal angle is 120 degrees, so each external angle is 60 degrees.

Advanced Usage

• "Exterior angle": This is a common synonym for "external angle" and is used interchangeably in geometry.
  • The theorem states that an exterior angle of a triangle is equal to the sum of the two opposite interior angles.

Variants and Related Words

• Exterior angle (n): A synonym for external angle.
• Interior angle (n): The angle inside a polygon at a vertex. The interior and external angles are supplementary.
• Supplementary angles (n): Two angles whose measures sum to 180 degrees. An external angle and its adjacent interior angle are supplementary.

Synonyms

• Exterior angle: The most direct synonym.
• Outer angle: A less common but descriptive synonym.

Related Phrases

• Remote interior angles: In a triangle, the two interior angles that are not adjacent to a given exterior angle.

Noun

1. the supplement of an interior angle of a polygon