Question

answer if you are genius​

Answer 1

Answer:

Sum of interior and exterior angle should be 180°

let us say interior angle = 2x and exterior angle = x

2x+x=180

x = 60°

int angle = 120°

ext angle = 60°

ext angle of a polygon = 360°/n

60 = 360/n

n = 6

polygon has 6 side. so hexagon

Answer 2

Question :

How many sides does a regular polygon have whose interior and exterior angles are in the ratio 2 : 1 ?

(1) 3

(2) 5

(3) 6

(4) 12

Answer:

The Number of sides are 6.

Step-by-step explanation:

Given :

Ratio of exterior and interior angles = 2 : 1

To find :

The sides of the polygon

Solution :

Let the angles be -

• Interior angle as 2y
• Exterior angle as y

We are familiar with the fact that sum of interior and exterior angles is 180°

⇒ 2y + y = 180

⇒ 3y = 180

⇒ y = 180/3

⇒ y = 60

Exterior angle = 60°

$\rule{300}{1.5}$

Number of sides -

★ Exterior angle = 360/n (where n is the Number of sides)

⇒ 60 = 360/n

⇒ n = 360/60

⇒ n = 6

Side = 6

$\therefore$ The Number of sides are 6.