Question

if the ratio between an exterior angle and interior angle is 1:5 then the number of sides of a regular polygon is?

Pls help I don't understand how to solve it and not only help but also explain me in detail I would kindly appreciate help explaining me this in detail ​

Answer 1

Answer:

The ratio between the interior angles and exterior angles of a regular polygon is 5:1, what is the number of sides of the polygon?

Let number of sides of the polygon = n. Acordingly:-

exterior angle =360°/n…………(1)

Therefore interior angle =180° -(360°/n)=(n-2).180°/n………..(2)

{(n-2).180°/n}/{360°/n}= 5/1

(n-2)/2 = 5/1

n-2= 10

or. n=12. sides. Answer.

Second-method:-

Let interior angle and exterior angle of a polygon are. 5x° and x° respectively.

5x+x=180°

6x=180°. => x= 30°. [exterior angle is 30°]

But. exterior angle = 360°/n

Therefore. 360°/n=30° => n = 360°/30°. = 12 sides.

Answer 2

Answer:

Let the exterior angle and interior angle be x and 5x,respectively.

Then,x+5x=180

6x=180

x=180/6

x=30

The number of sides=360/exterior angle

=360/30=12

Step-by-step explanation:

Hope it helps you.