Question 236995
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.