Obtuse angle
High School
Definition
A angle that measures greater than 90° but less than 180°. In other words it is an angle between a right angle and a straight line. It is the biggest out of the three main angle categories (obtuse angle, right angle, acute angle).
Worked examples
\(120^\circ\) is obtuse
This angle is greater than \(90^\circ\) but less than \(180^\circ\), so it is obtuse.
\(95^\circ\) is obtuse, \(90^\circ\) is right, \(85^\circ\) is acute
An obtuse angle is just barely wider than a right angle and reaches up to a straight line.
Common mistakes
- \(180^\circ\) is obtuse → \(180^\circ\) is a straight angle, not obtuse Obtuse angles must be less than \(180^\circ\); a straight angle is exactly \(180^\circ\).
- Any angle bigger than \(90^\circ\) is obtuse → Only angles between \(90^\circ\) and \(180^\circ\) are obtuse Angles \(180^\circ\) or larger (reflex angles) are not obtuse.
- \(89^\circ\) is obtuse because it is close to \(90^\circ\) → \(89^\circ\) is acute; obtuse is greater than \(90^\circ\) An angle must be strictly greater than \(90^\circ\) to be obtuse.
Where you'll use it next
You'll classify obtuse angles when studying triangle types, polygon interior angles, and trigonometry, and when proving angle relationships in geometry.
Found in 1 StudyPug lesson
Mastering Triangle Classification: Your Key to Geometry Success
10th Grade10thGeometry
Unlock the world of geometry by mastering triangle classification. Learn to identify and understand various triangle types, their properties, and real-world applications. Boost your problem-solving skills today!
See also
Reviewed by Pat Cheng, M.Ed. — StudyPug Curriculum Lead · Last updated June 6, 2026