Question

The ratio of an interior angle to be exterior angle of a regular polygon is 5: 1 find the number of sides of the polygon

Answer 1

Hi friend!!

Let 5x be the interior angle of a regular polygon and x be the exterior angle of a regular polygon.

Since the two angles are linear angles. Their sum is 180°

→5x+x=180

6x=180

x=30°

Interior angle of the regular polygon is 150° and exterior angle of the regular polygon is 30°

Interior angle of a n sided regular polygon is

2(n-2)×90/n=150

n-2/n=15/18

18n-36=15n

3n=36

n=12

The polygon is of 12 sides.


I hope this will help you;)

Answer 2

Heya Dear,

           ____________________________

Let x is included in the ratio.

Interior angle = 5 x.

Exterior angle = x.

We know that those angles will be pair of linear angles.

⇒ 5x + x = 180°

⇒ 6x = 180°

⇒ x = 180° / 6

∴  x = 30°.

Each interior angle = 5 x = 5 × 30° = 150°.

Each interior angle of a regular polygon = 2 ( n - 2 ) × 90° / n

⇒ 150° = 180° ( n - 2 ) / n

⇒ 150° n = 180° n - 360°

⇒ 180° n - 150° n = 360°

⇒ 30° n = 360°

⇒ n = 360° / 30°

∴  n = 12.

The required answer is 12.


Hope it helps !