UPSC 2015 CDS I Math Paper

Let the number of sides of the polygon be n
Formula:
Each interior angle of the regular polygon
=

(n−2)×180°

n

∴

(n−2)×180°

n

=135°
⇒180n−135n=360
⇒45n=360
⇒n=8
The number of vertices of the polygon = The number of sides of the polygon = n = 8
Formula:
The number of diagonals of the polygon of side n=

n(n−3)

2

Therefore, the number of diagonals of the polygon =

n(n−3)

2

=

8×5

2

=20