Regular polygons
A quadrilateral inscribed in a circle, so that all its vertices lie on the circumference is called a cyclic quadrilateral.
The opposite angles of a cyclic quadrilateral are supplementary.

 a + g = b + d = 180°, d1 · d2  = a  ·  c + b · d perimeter    P = a + b + c + d,     s = 1/2P area
A quadrilateral whose sides all lie tangent to the circle inscribed within the quadrilateral is called a tangential quadrilateral.

 s = a + c = b + d, perimeter    P = a + b + c + d,     s = 1/2P area A = r · s
Polygons
A polygon is closed plane figure bounded by a number of straight line segments with the same number of vertices.
The sum of interior angles is  (n - 2) · 180°, where n is the number of sides of a polygon.
The sum of exterior angles of a polygon is 360°.

 dn - number of diagonals b' - the exterior angle dn = 1/2 · n · (n - - 3) Sn= (n - 2) · 180° - the sum of interior angles
Regular polygons
In a regular polygon all sides are equal and all its angles are equal.
The exterior angle of a regular polygon is b' = 360°/n, where n is the number of sides of a regular polygon. .
 a = b' = 360°/n b' - the exterior angle b = 180° - b' = (n - 2) · 180°/n, P = n · a dn = 1/2 · n · (n - - 3) - number of diagonals A = 1/2 · n · a · r = 1/2P · r - area of a regular polygon
Beginning Algebra Contents D