exterior angle
LowTechnical / Academic
Definition
Meaning
An angle formed between one side of a polygon and the extension of an adjacent side.
In geometry, the angle that is outside a polygon, typically measured when a side of the polygon is extended. More generally, can refer to any angle facing outward or situated on the outside.
Linguistics
Semantic Notes
The term is almost exclusively used in mathematical geometry. Its meaning is precise and unambiguous within that context. The sum of the exterior angles of any convex polygon is always 360 degrees.
Dialectal Variation
British vs American Usage
Differences
No significant lexical or conceptual differences. Terminology and definitions are identical in both mathematical traditions.
Connotations
Neutral, purely technical term.
Frequency
Equally low frequency in both UK and US English, confined to educational and professional mathematical contexts.
Vocabulary
Collocations
Grammar
Valency Patterns
The exterior angle of [a triangle/polygon]An exterior angle is formed by [extending a side]Vocabulary
Synonyms
Neutral
Weak
Vocabulary
Antonyms
Usage
Context Usage
Business
Extremely rare to non-existent.
Academic
Exclusively used in mathematics education and geometry textbooks.
Everyday
Virtually never used outside of a maths lesson.
Technical
Standard term in Euclidean geometry and related fields.
Examples
By Part of Speech
adjective
British English
- The exterior-angle measurement is crucial.
- We studied the exterior-angle theorem.
American English
- The exterior-angle measurement is key.
- We learned the exterior-angle theorem.
Examples
By CEFR Level
- Look at this shape. The angle outside is the exterior angle.
- In a triangle, each exterior angle is equal to the sum of the two opposite interior angles.
- To find the size of one exterior angle of a regular polygon, you divide 360 degrees by the number of sides.
- The proof hinges on the theorem that the sum of the exterior angles of any convex polygon is invariably 360 degrees, regardless of the number of sides.
Learning
Memory Aids
Mnemonic
Imagine standing outside (EXTERIOR) a house and looking at the corner from the outside. That's your view of the exterior angle.
Conceptual Metaphor
ANGLE AS SPACE; GEOMETRIC SHAPES AS BOUNDED TERRITORIES (inside vs. outside).
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- "Внешний угол" is a direct translation and correct. No significant trap, but ensure understanding of the precise geometric construction (extending a side).
Common Mistakes
- Confusing it with the interior angle.
- Forgetting that an exterior angle is supplementary to its adjacent interior angle.
- Thinking an exterior angle is only measured from the vertex outwards, not understanding it's formed by a side and the extension of another side.
Practice
Quiz
What is the sum of the exterior angles of a convex pentagon?
FAQ
Frequently Asked Questions
Not necessarily. An exterior angle is supplementary to its adjacent interior angle, so if the interior angle is acute (<90°), the exterior angle will be obtuse (>90°).
Yes, there are two exterior angles at each vertex (one on each side of the extension of a side), but they are vertical angles and therefore equal in measure.
No, the term is specific to plane geometry and polygons. In 3D geometry, you would discuss dihedral angles or face angles.
Yes, all polygons, regular or irregular, have exterior angles. The theorem that their sum is 360° holds true for all simple convex polygons.