Obtuse Angle

Pronunciation: /əbˈtus ˈæŋ.gəl/ Explain

Obtuse Angles
Figure 1: Obtuse angles measure > 90° and <180°

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 four classes according to their measure. An obtuse angle is an angle that measures more than 1/4 of a full circle and less than 1/2 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, obtuse angle. 2nd Classroom edition 20150108-4799968. pg 128. 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 3. www.archive.org. D. Van Nostrand Company. 1908. Last Accessed 9/5/2018. http://www.archive.org/stream/mathengineer00kellrich#page/3/mode/1up/search/obtuse. Buy the book
  3. Casey, John, LL.D., F.R.S.. The First Six Books of the Elements of Euclid. pg 7. www.archive.org. Casey, John, LL.D. F.R.S.. Hodges, Figgis & Co.. 1890. Last Accessed 9/5/2018. http://www.archive.org/stream/firstsixbooksofe00caseuoft#page/7/mode/1up/search/obtuse. Buy the book

More Information

  • McAdams, David E.. Angle. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 3/12/2009. https://www.allmathwords.org/en/a/angle.html.

Cite this article as:

McAdams, David E. Obtuse Angle. 4/27/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/o/obtuseangle.html.

Image Credits

Revision History

4/27/2019: Changed equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
9/5/2018: Removed broken links, updated license, implemented new Geogebra protocol, implemented new markup. (McAdams, David E.)
8/7/2018: Changed vocabulary links to WORDLINK format. (McAdams, David E.)
1/1/2010: Added "References". (McAdams, David E.)
12/21/2009: 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.)
8/26/2008: Added entries to 'More Information'. (McAdams, David E.)
7/12/2007: Initial version. (McAdams, David E.)

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