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 =