Geometry-Polygons

Geometry-Polygons

13.The interior angle sum property: The sum of the angles of a quadrilateral is  or 4 right angles.

\( \left| \!{\underline {\, A \,}} \right. + \left| \!{\underline {\, B \,}} \right. + \left| \!{\underline {\, C \,}} \right. + \left| \!{\underline {\, D \,}} \right. = 360^0 \)
Note: 
(i) If there is a polygon of n sides \( (n \geqslant 3) \), we can cut it up in to (n-2) triangles, with a common vertex.
(ii) The sum of all the interior angles of a polygon of n sides would be \( (2n - 4) \) right angles.
(iii) If there is a regular polygon of n sides \( (n \geqslant 3) \), then its each interior angle is equal to \( \left( {\frac{{2n - 4}} {n}} \right) \) right angles (i.e) \( \left( {\frac{{2n - 4}} {n}x 90} \right)^0 \)

14. Exterior angle sum property : If the sides of a quadrilateral are produced in order the sum of four exterior angles so formed is \( 360^0 \)

\( \left| \!{\underline {\, 1 \,}} \right. + \left| \!{\underline {\, 2 \,}} \right. + \left| \!{\underline {\, 3 \,}} \right. + \left| \!{\underline {\, 4 \,}} \right. = 360^0 \)
Note: 
 (i) The sum of all the exterior angles formed by producing the sides of a covex polygon in the same order is equal to four right angles.

\( \left| \!{\underline {\, 1 \,}} \right. + \left| \!{\underline {\, 2 \,}} \right. + \left| \!{\underline {\, 3 \,}} \right. + \left| \!{\underline {\, 4 \,}} \right. + \left| \!{\underline {\, 5 \,}} \right. = 360^0 \)
(ii) Each exterior angle of a regular polygon of n sides is equal to \( \left( {\frac{{360}} {n}} \right)^0 \)