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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