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

## 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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