Rectilinear Figures


   
 
Theorem 1
In a polygon of 'n' sides, the sum of the interior angles is equal to (2n - 4) right angles.
 
 
ABCDE is an n sided polygon.
 
 
The sum of the interior angles = (2n - 4) right angles
 
 
Take any point O inside the polygon. Join OA, OB, OC.
 
 
 
 
 
Sum of 'n' interior angles = (2n - 4) 90o.
 
Each interior angle of a regular polygon
 
 
[Since in a regular polygon, all the interior angles are equal].
 
 
If the sides of a convex polygon are produced in order (clockwise or anticlockwise), the sum of the exterior angles is 4 right angles.
 
= 4 right angles = 4 90o
 
 
Each exterior angle for a regular polygon of n sides
 
Number of sides of a regular polygon
 
 
2. At each vertex, one interior angle + one exterior angle = 180o.
 
 
 
How many sides has a regular polygon with each interior angle equal to 144o?
 
 
[Each interior angle + each exterior angle = 180o]
 
144o + each exterior angle = 180o
 
each exterior angle = 180o - 144o
 
= 36o.
 
Number of sides
 
 
= 10
 
 
 
The sum of the interior of a regular polygon is 1080o. How many sides are there?
 
 
The sum of the interior angles
 
= (2n - 4) x 90o
 
= 1080o
 
(2n - 4) x 90 = 1080
 
2n - 4 =
 
2n = 16
 
n = 8
 
The polygon has 8 sides.
 
 
     
   
Get FREE Live Tutoring
Get FREE Live Tutoring
(No credit card required)

Customer Care

Click to get customer service, technical support and subscription help.

Customer Care Chat


Refer-A-Friend

Get One Month Free!
When you refer a friend