Sum of the interior angles of a polygon
The sum of the interior angles of a polygon is
180 ( n — 2 ) °
where n is the number of sides the polygon has.
Sum of the exterior angles of a polygon
The sum of the exterior angles of a polygon is 360°.
For a regular polygon that has n sides, each exterior angle is
Angles in opposite segments of a cyclic quadrilateral
The opposite angles of a cyclic quadrilateral are supplementary, i.e. 180°.
a + b = 180°
c + d = 180°
Exterior angle in a cyclic quadrilateral
The exterior angle of a cyclic quadrilateral is equal to the interior opposite angle.
<B = <D