Art of Problem Solving

Interior angle: Difference between revisions

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The '''interior angle''' is the [[angle]] between two line segments, having two endpoints connected via a path, facing the path connecting them.
The '''interior angle''' is the [[angle]] between two line segments, having two endpoints connected via a path, facing the path connecting them.


The regular polygons are formed by have all interior angles [[equiangular]]  
All of the interior angles of a [[regular polygon]] are congruent (in other words, regular polygons are [[equiangular]]).
 
This is the complementary concept to [[exterior angle]]


==Properties==
==Properties==


#All the interior angles of an <math>n</math> sided regular polygon, sum to <math>(n-2)180</math> degrees.
#All the interior angles of an <math>n</math> sided regular polygon sum to <math>(n-2)180</math> degrees.
 
#All the interior angles of an <math>n</math> sided regular polygon are <math>180(1-{2\over n})</math> degrees.
#All the interior angles of an <math>n</math> sided regular polygon,are <math>180(1-{2\over n})</math> degrees.
#As the interior angles of an <math>n</math> sided regular polygon get larger, the ratio of the [[perimeter]] to the [[apothem]] approaches <math>2\pi</math>.


#As the interior angles, of an <math>n</math> sided regular polygon get larger, the ratio of the [[perimeter]] to the [[apothem]] approaches <math>pi</math>
== See Also ==
* [[Exterior angle]]

Latest revision as of 09:02, 1 August 2024

The interior angle is the angle between two line segments, having two endpoints connected via a path, facing the path connecting them.

All of the interior angles of a regular polygon are congruent (in other words, regular polygons are equiangular).

Properties

  1. All the interior angles of an $n$ sided regular polygon sum to $(n-2)180$ degrees.
  2. All the interior angles of an $n$ sided regular polygon are $180(1-{2\over n})$ degrees.
  3. As the interior angles of an $n$ sided regular polygon get larger, the ratio of the perimeter to the apothem approaches $2\pi$.

See Also