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Answer to Question #21311 in Geometry for ronielle jackson

Question #21311
the polygon angle-sum theorem states ?
Expert's answer
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 alwaysequal to 360 degrees.

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

each interior angle of a regular polygon is equal to thesum of the angles divided by the number of sides.
for a regular triangle, each interior angle is equal to180/3 = 45.

for a regular quadrilateral, each interior angle is equalto 360/4 = 90 degrees.
a regular polygon has each interior angle equal to eachother.
for a regular triangle, each interior angle = 60 degreesand each exterior angle = 180-60 = 120 degrees. sum of exterior angles is equal
to 3 * 120 = 360.

for a regular quadrilateral (square / rectangle) eachexterior 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 ofexterior angles = 5 *
72 degrees = 360 degrees.

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