Supplementary angles
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It has been suggested that this article be merged with Complementary angles, Vertical angles, Adjacent angles and Transversal (geometry) to Special angle relationships. (Discuss) Proposed since December 2011. |
Supplementary angles are pairs of angles that add up to 180 degrees. Thus the supplement of an angle of x degrees is an angle of (180 − x) degrees.
If the two supplementary angles are adjacent (i.e. have a common vertex and share just one side), their non-shared sides form a straight line. However, supplementary angles do not have to be on the same line, and can be separated in space. For example, adjacent angles of a parallelogram are supplementary, and opposite angles of a cyclic quadrilateral (one whose vertices all fall on a single circle) are supplementary.
If a point P is exterior to a circle with center O, and if the tangent lines from P touch the circle at points T and Q, then ∠TPQ and ∠TOQ are supplementary.
Trigonometric ratios [edit]
The sines of supplementary angles are equal. Their cosines and tangents (unless undefined) are equal in magnitude but have opposite signs.
See also [edit]
External links [edit]
- Animated demonstration - Interactive applet and explanation of the characteristics of supplementary angles.
- Angle definition pages with interactive applets that are also useful in a classroom setting. Math Open Reference
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