obtuse angle
Low-mediumFormal, Academic, Technical
Definition
Meaning
A geometrical angle that measures greater than 90 degrees and less than 180 degrees.
A figurative term for a lack of sharpness or perceptiveness in a person's understanding; in mathematics, a type of triangle classified by having one angle greater than 90 degrees.
Linguistics
Semantic Notes
Primary meaning is strictly mathematical. Its figurative use meaning 'slow to understand' stems from the metaphorical link between 'sharp' (acute) intellect and 'dull' (obtuse) intellect.
Dialectal Variation
British vs American Usage
Differences
No significant difference in meaning or usage; it is a standard international mathematical term.
Connotations
Identical in both varieties; the figurative use ('obtuse person') is understood but slightly less common than the literal geometric meaning.
Frequency
Used exclusively in scientific, mathematical, and educational contexts in both regions.
Vocabulary
Collocations
Grammar
Valency Patterns
The triangle contains an obtuse angle.An obtuse angle measures between 90 and 180 degrees.Vocabulary
Synonyms
Neutral
Weak
Vocabulary
Antonyms
Usage
Context Usage
Business
Rarely used; only in very specific technical or design discussions.
Academic
Common in geometry, trigonometry, engineering, and physics textbooks and lessons.
Everyday
Uncommon in casual conversation unless discussing math homework or technical DIY.
Technical
Standard, precise term in all fields of mathematics, drafting, and design.
Examples
By Part of Speech
adjective
British English
- The triangle has an obtuse angle.
- His obtuse remarks failed to address the core issue.
American English
- The triangle has an obtuse angle.
- She found his criticism to be deliberately obtuse.
Examples
By CEFR Level
- Look at this shape. This is an obtuse angle.
- An obtuse angle is bigger than a right angle.
- In geometry class, we learned to identify an obtuse angle using a protractor.
- A triangle can only have one obtuse angle.
- The architect specified that the corner should form an obtuse angle to soften the building's appearance.
- His obtuse refusal to acknowledge the data frustrated the entire research team.
- The proof hinges on the property that the cosine of an obtuse angle is negative.
- Her deliberately obtuse line of questioning seemed designed to obfuscate rather than clarify.
Learning
Memory Aids
Mnemonic
Think: 'obtuse' sounds like 'ob-stuse' – it's too big and 'stuck' being blunt, unlike a sharp, acute angle.
Conceptual Metaphor
INTELLIGENCE IS SHARPNESS (therefore, lack of intelligence is 'obtuseness').
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- Direct translation of 'obtuse' as 'тупой' works for the angle, but beware: calling a person 'obtuse' (figuratively) translates directly and is understood, though it's a formal/literary usage in English.
Common Mistakes
- Confusing with 'acute angle' (less than 90°).
- Stating 'obtuse angle is 90 degrees' (it is *greater than* 90).
- Using 'obtuse' to mean 'obscure' or 'hard to see' (incorrect).
Practice
Quiz
What is the precise range of an obtuse angle?
FAQ
Frequently Asked Questions
No, it is impossible. The sum of angles in any triangle is 180°. Two obtuse angles (each >90°) would already sum to more than 180°.
'Obtuse' means blunt or slow to understand (or, in math, an angle >90°). 'Abstruse' means difficult to comprehend, often because of complexity.
No. An obtuse angle is strictly *greater than* 90° and *less than* 180°. A 180° angle is a straight angle.
The phrase itself is not typically used figuratively. The adjective 'obtuse' is used figuratively (e.g., 'an obtuse person'), but the full noun phrase 'obtuse angle' retains its literal, mathematical meaning.