1. The sum of the angles of
a polygon is xº. What is
the sum of the angles of a
polygon with 2 more sides?
Answers
8th
Maths
Understanding Quadrilaterals
The sum of the interior angles of a polygon of n sides is equal
ANSWER
It is given that ABCDE is n sided polygon.
Take any point O inside the polygon and join OA,OB and OC.
The polygon forms 'n' triangles as it is an 'n' sided polygon.
Since sum of the angles of the triangle is 180 degrees, therefore, sum of the angles of 'n' triangles is =n×180
0
which implies
Sum of interior angles + Sum of the angles at O =2n×90
0
..........(1)
But the sum of the angles at O is 360 degree ( angles around a point) ..........(2)
Therefore, from equations (1) and (2), we get
Sum of the interior angles + 360
0
=2n×90
0
=2n×90
0
−360
0
=90
0
(2n−4)
Thus, sum of the 'n' interior angles =(2n−4)×90
0
Therefore, each interior angle of a regular polygon =
n
(2n−4)×90
0
Hence, option C is correct.
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