Obtuse Angle

Pronunciation: /əbˈtus ˈæŋ gəl/ ?

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

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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[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

Click on the blue point in the manipulative and drag it to change the figure.

References

  1. Keller, Samuel Smith. Mathematics for Engineering Students, Plane and Solid Geometry, pg 3. D. Van Nostrand Company, 1908. (Accessed: 2010-01-02). http://www.archive.org/stream/mathengineer00kellrich#page/3/mode/1up/search/obtuse.
  2. Casey, John, LL.D., F.R.S.. The First Six Books of the Elements of Euclid, pg 7. Casey, John, LL.D. F.R.S.. Hodges, Figgis & Co., 1890. (Accessed: 2010-01-02). http://www.archive.org/stream/firstsixbooksofe00caseuoft#page/7/mode/1up/search/obtuse.
  3. obtuse angle. merriam-webster.com. Encyclopedia Britannica. (Accessed: 2009-12-21). http://www.merriam-webster.com/dictionary/obtuse angle.

More Information

  • McAdams, David. Angle. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Angle.
  • McAdams, David. Obtuse Triangle. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Obtuse Triangle.
  • McAdams, David. Acute Angle. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Acute%20Angle.

Cite this article as:


Obtuse Angle. 2010-01-01. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/o/obtuseangle.html.

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Revision History


2010-01-01: Added "References" (McAdams, David.)
2009-12-21: Added reference to Euclid's Elements; Expanded table of angle classes. (McAdams, David.)
2008-09-16: Changed text on classes of angles to a table. Changed images 2 and 3 to one manipulative (McAdams, David.)
2008-08-26: Added entries to 'More Information' (McAdams, David.)
2007-07-12: Initial version (McAdams, David.)

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