Acute Angle

Pronunciation: /əˈkyut ˈæŋ gəl/ ?

Acute Angles
Figure 1: Acute angles measure < 90°

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Angles are divided into four 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

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  1. acute angle. Encyclopedia Britannica. (Accessed: 2009-12-21). angle.
  2. Keller, Samuel Smith. Mathematics for Engineering Students, Plane and Solid Geometry, pg 2. D. Van Nostrand Company, 1908. (Accessed: 2010-01-02).
  3. Casey, John, LL.D., F.R.S.. The First Six Books of the Elements of Euclid, 10th Edition, pg 4. Casey, John, LL.D. F.R.S.. Hodges, Figgis & Co., 1890. (Accessed: 2010-01-02).

Printed Resources

Cite this article as:

Acute Angle. 2010-01-01. All Math Words Encyclopedia. Life is a Story Problem LLC.


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Revision History

2010-01-01: 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.)
2008-03-03: Revised other resources, added reference to radians (McAdams, David.)
2007-07-16: Expanded keyword 'acute' to include 'angle' (McAdams, David.)
2007-07-12: Initial version (McAdams, David.)

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