Question

find the number of sides of a polygon whose exterior and interior angles are in the ratio 2:7.​

Answer 1

☆ Solution ☆

Given :-

• Sides of a polygon whose exterior and interior angles are in the ratio 2:7.

To Find :-

• The number .

Step-by-Step-Explaination :-

As we know :-

Exterior angle + interior angle = 180°

Let the ratios be 2x and 7x

So,

2x + 7x = 180°

9x = 180°

x = 180/9

x = 20°

So,

Exterior angle of polygon is 2 × 20° = 40°

Now,

As we know that :-

Sum of all exterior angle = 360°

Let the number of polygon be x

So,

n × 40° = 360°

n = 360/40

n = 9

Hence,

The number of polygon = 9.

Answer 2

Answer:

Step-by-step explanation:

Solution ☆

Given :-

Sides of a polygon whose exterior and interior angles are in the ratio 2:7.

To Find :-

The number .

Step-by-Step-Explaination :-

As we know :-

Exterior angle + interior angle = 180°

Let the ratios be 2x and 7x

So,

2x + 7x = 180°

9x = 180°

x = 180/9

x = 20°

So,

Exterior angle of polygon is 2 × 20° = 40°

Now,

As we know that :-

Sum of all exterior angle = 360°

Let the number of polygon be x

So,

n × 40° = 360°

n = 360/40

n = 9

Hence,

The number of polygon = 9.