Question

name the polygon whose sum of interior angle is 1440

Answer 1

let the number of sides = n
we have
180(n-2)= 1440
n-2 = 8
n= 10
therefore the polygon has 10 sides aka decagon

Answer 2

we know that sum of interior angle of a polygon=2(n-2)×90°

here sum of interior angles=1440°

according to the question,

(2n-4)×90=1440

or,180n-360=1440

or,180n=1440+360

or,180n=1800

or,n=1800/18

or,n=10

therefore,name of the polygon is decagon

exterior angle of decagon=360°/n

exterior angle of decagon=360°/10=36°

diagonals of decagon=n(n-3)/2

diagonals of decagon=10(10-3/2=10×7/2=70/2=35

Decagon is polygon who has 10 sides