Acute angle
High School
Definition
An angle that is smaller than a right angle (90°). Acute means "sharp" so it may also be refered to as a "sharp" angle. A helpful way to help differenciate the different types of angles is to think of acute angles as "a cute" angle, meaning small and less than 90°. A triangle with three acute angles is known as a acute triangle.
Worked examples
\(45^\circ\) is acute because \(45^\circ < 90^\circ\)
Any angle measuring less than 90 degrees is acute.
\(89^\circ\) is acute, but \(90^\circ\) is right and \(91^\circ\) is obtuse
Even one degree at 90° or above makes it no longer acute.
Common mistakes
- \(120^\circ\) is acute → \(120^\circ\) is obtuse (greater than \(90^\circ\)) Acute means less than 90°; angles above 90° are obtuse.
- A \(90^\circ\) angle is acute → A \(90^\circ\) angle is a right angle, not acute Acute is strictly less than 90°; exactly 90° is the boundary.
- All small-looking angles are acute → Check the measure; appearance can be misleading Diagrams are not always to scale—use the degree measure to classify.
Where you'll use it next
You'll use acute angles when classifying triangles, solving problems with complementary angles, working with trigonometric ratios in right triangles, and analyzing geometric figures throughout geometry and trigonometry.
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