Acute Angle

Pronunciation: /əˈkyut ˈæŋ gəl/ Explain

Acute Angles
Figure 1: Acute angles measure < 90°

Find the angles in the manipulative that are acute angles.
Click on the blue point and drag it to change the figure.

Can you find all 5 angle classes represented?
Manipulative 1 - Angle Classes Created with GeoGebra.
Manipulative 1: Classes of angles. Click on the blue point in the manipulative and drag it to change the figure. Created with GeoGebra.
Click to see gadget Angle Class Classroom Demonstrator.

Angles are divided into six classes according to their measure. An acute angle is an angle that measures less than 1/4 of a full circle[1][2].

Classes of Angles
Degree MeasureRadian MeasureClass Name
α<90°α<π/2 rad. Acute angle
α=90°α=π/2 rad. Right angle
90°<α<180°π/2<α<π rad. Obtuse angle
α=180°α=π rad. Straight angle
180<α<360°π<α<2π rad. Reflex angle
α=360°α=2π rad. Full angle
Table 1: Classes of angles


  1. Keller, Samuel Smith. Mathematics for Engineering Students, Plane and Solid Geometry. pg 2. D. Van Nostrand Company. 1908. Last Accessed 8/6/2018. Buy the book
  2. Casey, John, LL.D., F.R.S.. The First Six Books of the Elements of Euclid. 10th Edition. pg 4. Hodges, Figgis & Co.. 1890. Last Accessed 8/6/2018. Buy the book

Cite this article as:

McAdams, David E. Acute Angle. 7/10/2018. All Math Words Encyclopedia. Life is a Story Problem LLC.

Image Credits

Revision History

6/12/2018: Removed broken links, changed Geogebra links to work with Geogebra 5, updated license, implemented new markup. (McAdams, David E.)
1/1/2010: Added reference to Euclid's Elements, Expanded table of angle classes. (McAdams, David E.)
9/16/2008: Changed text on classes of angles to a table. Changed images 2 and 3 to one manipulative (McAdams, David E.)
3/3/2008: Revised other resources, added reference to radians. (McAdams, David E.)
7/16/2007: Expanded keyword 'acute' to include 'angle'. (McAdams, David E.)
7/12/2007: Initial version. (McAdams, David E.)

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