Difference between exterior and interior angle a polygon is 120° (int

1.	Difference between exterior and interior angle a polygon is 120° (interior angle > exterior angle). Find the number of diagonals of the polygon.1. 422. 563. 544. 64
Answer» Correct Answer - Option 3 : 54 Given: Difference between exterior and interior angle a polygon is 120° (interior angle > exterior angle). Formula Used: 1. Each exterior angle of the polygon = 180° - Each interior angle of the polygon 2. Number of diagonals of regular polygon = [n (n – 3)] / 2 3. An exterior angle of polygon = 360°/n Where n = number of sides. Calculation: Let, the interior angle is x and exterior angle is y Accordingly, x - y = 120° ----(1) x + y = 180° ----(2) From (1) and (2) get, y = 30° and x = 150° The exterior of the given polygon is 30° The number of sides of the polygon = 360°/30° = 12 Number of diagonals of the polygon is {12 × (12 – 3)}/2 ⇒ (12 × 9)/2 = 54 ∴ The number of diagonals of the polygon is 54

Difference between exterior and interior angle a polygon is 120° (interior angle > exterior angle). Find the number of diagonals of the polygon.1. 422. 563. 544. 64

Answer» Correct Answer - Option 3 : 54

Given:

Difference between exterior and interior angle a polygon is 120° (interior angle > exterior angle).

Formula Used:

1. Each exterior angle of the polygon = 180° - Each interior angle of the polygon

2. Number of diagonals of regular polygon = [n (n – 3)] / 2

3. An exterior angle of polygon = 360°/n

Where n = number of sides.

Calculation:

Let, the interior angle is x and exterior angle is y

Accordingly,

x - y = 120° ----(1)

x + y = 180° ----(2)

From (1) and (2) get,

y = 30° and x = 150°

The exterior of the given polygon is 30°

The number of sides of the polygon

= 360°/30° = 12

Number of diagonals of the polygon is {12 × (12 – 3)}/2

⇒ (12 × 9)/2 = 54

∴ The number of diagonals of the polygon is 54