Answers

  • Brainly User
2015-11-12T22:59:49+08:00
Sum of interior angles in a polygon = 180 (n-2)  where n = number of sides

A ten-sided polygon, obviously, has 10 sides (decagon).

The sum of the interior angles of decagon = 180 (n-2)
                                                             = 180 (10-2)
                                                             = 180 (8)
                                                             =  1,440 degrees

Explanation of the pattern:
Why n-2?  
It is the expression in finding the number of triangles in a polygon, where n=number of sides. The sum of interior angles of triangle is 180 degrees.  Multiply 180 degrees by the number of triangles in a polygon yields the sum of the interior angles of the same polygon.


Decagon has 8 triangles inside it (10 sides - 2).  Multiply the number of triangles by 180 degrees, the result is 1,440 degrees.
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