If the sum of interior angles of a polygon is 1080°, what is the number of diagonals in it?

Given:

The sum of interior angles of a polygon = 1080°

Formula used:

The sum of interior angles of a polygon = (n – 2)180°

Number of diagonals = [n(n – 3)]/2

Here,

n = number of sides

Calculation:

The sum of interior angles of a polygon = 1080°

⇒ (n – 2)180° = 1080°

⇒ n – 2 = 6

⇒ n = 8

⇒ Number of diagonals = [n(n – 3)]/2

⇒ Number of diagonals = (8 × 5)/2 = 20

∴ Required answer is 20.