SOLUTION: the polygon angle-sum theorem states: the sum of the measures of the angles of an n-gon is___

SOLUTION: the polygon angle-sum theorem states: the sum of the measures of the angles of an n-gon is____ ?

Question 236995: the polygon angle-sum theorem states: the sum of the measures of the angles of an n-gon is____ ?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the sum of the INTERIOR angles of a polygon is equal to (n-2) * 180 where n is equal to the number of sides.

sum of the interior angles of a triangle = 3 sides = (3-2) * 180 = 180

sum of the interior angles of a quadrilateral = 4 sides = (4-2) * 180 = 360 degrees.

the sum of the EXTERIOR angles of a polygon is always equal to 360 degrees.

The exterior angle of a polygon is equal to the supplement of the interior angle of a polygon.

each interior angle of a regular polygon is equal to the sum of the angles divided by the number of sides.

for a regular triangle, each interior angle is equal to 180/3 = 45.

for a regular quadrilateral, each interior angle is equal to 360/4 = 90 degrees.

a regular polygon has each interior angle equal to each other.

for a regular triangle, each interior angle = 60 degrees and each exterior angle = 180-60 = 120 degrees. sum of exterior angles is equal to 3 * 120 = 360.

for a regular quadrilateral (square / rectangle) each exterior angle = 180 - 90 = 90 degrees. sum of exterior angles is equal to 4 * 90 = 360.

this works for all polygons up to n sides.

for a pentagon, sum of interior angles = (5-2) * 180 = 540 degrees. each interior angle = 540 / 5 = 108 degrees.
each exterior angle = (180-108) = 72 degrees. sum of exterior angles = 5 * 72 degrees = 360 degrees.

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