This is the "11.1: Angle Measures in Polygons" page of the "Geometry Chapter 11" guide.
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Geometry Chapter 11   Tags: geometry, mahlman, math  

Last Updated: Feb 19, 2014 URL: http://libguides.mpsaz.net/content.php?pid=104790 Print Guide RSS Updates

11.1: Angle Measures in Polygons Print Page
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Theorem

     
ShapeSidesSum of
Internal Angles
ShapeEach Angle
Triangle 3 180° triangle 60°
Quadrilateral 4 360° Quadrilateral 90°
Pentagon 5 540° Pentagon 108°
Hexagon 6 720° Hexagon 120°
Heptagon (or Septagon) 7 900° 128.57...°
Octagon 8 1080° 135°
... ... .. ... ...
Any Polygon n (n-2) × 180° (n-2) × 180° / n

 

 

Example: What about a Regular Decagon (10 sides) ?

Sum of Internal Angles

= (n-2) × 180°

 

= (10-2)×180° = 8×180° = 1440°


And it is a Regular Decagon so:

Each internal angle = 1440°/10 = 144°

 
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