Acute Angle

Pronunciation: /əˈkjut ˈæŋ.gəl/ Explain

Acute Angles
Figure 1: Acute angles measure < 90°

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.

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[2][3].

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. McAdams, David E.. All Math Words Dictionary, acute angle. 2nd Classroom edition 20150108-4799968. pg 10. Life is a Story Problem LLC. January 8, 2015. Buy the book
  2. Keller, Samuel Smith. Mathematics for Engineering Students, Plane and Solid Geometry. pg 2. D. Van Nostrand Company. 1908. Last Accessed 6/12/2018. Buy the book
  3. 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 6/12/2018. Buy the book

Cite this article as:

McAdams, David E. Acute Angle. 4/11/2019. All Math Words Encyclopedia. Life is a Story Problem LLC.

Image Credits

Revision History

4/11/2019: Changed equations and expressions to new format. (McAdams, David E.)
1/7/2019: Removed extraneous text about manipulative. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
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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