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