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The sum of the interior angles of a triangle is 180º; of a quadrilateral is 360º and of a pentagon is 540º. Assuming this pattern continues, what is the sum of the interior angles of a 10-sided polygon?

Sagot :

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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