The sum of interior angles of a polygon is 2700°. How many sides the polygon has ?

Question

The sum of interior angles of a polygon is 2700°. How many sides
the polygon has ?

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Aubrey 2 weeks 2021-09-13T21:44:33+00:00 1 Answer 0 views 0

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    2021-09-13T21:46:08+00:00

    the sum of the interior angles of a polygon is given by the equation:  

    s = (n-2)*180 where:  

    s = the sum of the interior angles.

    n = the number of sides of the polygon.  

    given that s = 2700, this equation becomes:  

    2700 = (n-2)*180  

    simplify to get:  

    2700 = 180*n – 360  

    add 360 to both sides of this equation to get:  

     

    3060 = 180*n  

    divide both sides of this equation by 180 to get:  

    n = 3060/180 = 17  

    the polygon has 17 sides.  

    each interior angle of this polygon = 2700/17 = 158.8235294  

    each exterior angle of this polygon = 180 – 158.8235294 = 21.17647059  

    17 * 21.17647059 = 360 degrees which is should since the sum of the exterior angles of a polygon is always 360 degrees

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