Question

the ratio of an interior angle to the exterior angle of a regular polygon is 5:1 the number of side of polygon is?

Answer 1

Answer:

12

Step-by-step explanation:

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.

Answer 2

Given : The ratio of of an interior angle to the exterior angle of a regular polygon is 5:1

To find : The number of sides of the regular polygon.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the number of sides of the polygon)

Let,

The interior angle of the regular polygon = 5x°

and, the exterior angle of the regular polygon = x°

(obtained from the ratio 5:1)

Now,

Sum of an exterior angle and an interior of angle of a regular polygon is always equal to 180°

So,

5x + x = 180

6x = 180

x = 180/6

x = 30

An interior angle of the regular polygon = 5x° = (5 ×30)° = 150°

Let, the number of sides of the regular polygon = n

Now,

An interior angle of the regular polygon :

$= \frac{(n - 2)}{n} \times 180°$

By, comparing the two values of an interior angle of the regular polygon, we get :

$\frac{(n - 2)}{n} \times 180 = 150$

$\frac{(n - 2)}{n} = \frac{150}{180}$

$180n - 360 = 150n$

$180n - 150n = 360$

$30n = 360$

$n = \frac{360}{30}$

$n = 12$

So, the number of sides of the regular polygon = n = 12

(This will be considered as the final result.)

Hence, the number of sides of the regular polygon is 12