re-entering angle
Very Low (specialised technical term)Formal / Technical
Definition
Meaning
An internal angle of a polygon that points inward, greater than 180 degrees.
In geometry, an interior angle that is concave, creating an indentation in the shape's outline.
Linguistics
Semantic Notes
Primarily used in geometry, surveying, and architecture. The opposite of a 'salient angle.'
Dialectal Variation
British vs American Usage
Differences
Spelling and pronunciation may vary ('re-entering' vs 'reentering'), but the technical meaning is identical. US texts more often use the hyphenless 'reentering'.
Connotations
None beyond the technical definition.
Frequency
Equally rare in both varieties, confined to highly technical contexts.
Vocabulary
Collocations
Grammar
Valency Patterns
The polygon [has/contains] a re-entering angle.A re-entering angle [is formed/occurs] at vertex C.Vocabulary
Synonyms
Strong
Neutral
Weak
Vocabulary
Antonyms
Phrases
Idioms & Phrases
- “None”
Usage
Context Usage
Business
Not used.
Academic
Used in geometry, architecture, or land surveying textbooks and papers.
Everyday
Virtually never used.
Technical
Primary context: precise description of polygonal shapes in geometry, CAD, cartography, and fortification design.
Examples
By Part of Speech
verb
British English
- The boundary re-enters the plot, creating a re-entering angle.
American English
- The property line reenters at the northwest corner.
adverb
British English
- The wall turns re-enteringly at that point.
American English
- (Adverbial use is exceptionally rare and non-standard.)
adjective
British English
- We identified the re-entering angle vertex on the map.
American English
- The survey noted the reentering angle boundary.
Examples
By CEFR Level
- (Not applicable for this level.)
- (Not applicable for this level.)
- A star shape has many re-entering angles.
- The old castle wall was built with a re-entering angle for defence.
- The cartographer highlighted the re-entering angle where the parish boundary dipped inwards.
- Calculating the area of a polygon with one or more re-entering angles requires a different formula.
Learning
Memory Aids
Mnemonic
Think 'RE-enter' – the angle makes the shape's boundary dip back IN towards the centre, as if re-entering the shape's interior space.
Conceptual Metaphor
ANGLES ARE DIRECTIONS; a re-entering angle is a direction pointing back into the territory of the shape.
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- Avoid translating as 'повторный входной угол'. The standard Russian equivalent is 'внутренний угол' (when >180°) or более specifically 'вогнутый угол'.
Common Mistakes
- Confusing it with any angle less than 180°. It specifically must be *greater* than 180°.
- Using it to describe an angle in a triangle (impossible, as triangles are convex).
Practice
Quiz
In which shape would you MOST LIKELY find a re-entering angle?
FAQ
Frequently Asked Questions
In many contexts, yes. 'Reflex angle' is the general term for any angle between 180° and 360°. 'Re-entering angle' is often used specifically for the interior reflex angle of a concave polygon.
No. By definition, a triangle's interior angles always sum to 180°, so no single interior angle can exceed 180°. Triangles are always convex.
Mainly in technical drawing, land surveying (describing irregular plot boundaries), architecture, and the design of fortifications (where re-entering angles created defensive advantages).
A 'salient angle' or 'convex angle'—an interior angle less than 180° that projects outward from the polygon.