POLYGON POSTULATES AND THEOREMS
Quadrilateral Sum Postulate The sum of
the measures of the four angles of any
quadrilateral is 360°.
Polygon Sum Postulate The sum of the
measures of the n interior angles of an
n-gon
is 180°(n - 2).
Equiangular Polygon Postulate You can
find the measure of each interior angle
of an
equiangular n-gon with this formula:
180(n  2)
n
A Hexagon has 6 sides, and the diagonals
divde the the hexagon into 4 triangles.
Therefore, the diagonals of a polygon with
n sides make n-2 triangles, so the sum of
the interior angles is 180(n-2). If a
polygon is regular (or equilateral and equiangular), then each
interior angle is just the sum of the interior angles divided by the
number of sides.
Exterior Angle Sum Postulate For any
polygon, the sum of the measures of a set
of
exterior angles is 360°.
Regular Polygon Exterior Angle
Postulate
Each exterior angle of a n-sided regular
polygon is 360°/n
Diagonal Postulate
The number of diagonals of a n-sided
polygon is
n(n-3)/2
Exterior Angle = 360°/n