Question

The exterior angle of a regular polygon is one-fifth of its interior angle. How many sides have

the polygon​

Answer 1

Step-by-step explanation:

The sum of the interior angles of a polygon with n sides is:

(n − 2) * 180

And the sum of the exterior angles of a polygon is always 360°

Thus in this case:

1/5 * (n - 2) * 180 = 360

1/5 * (n - 2) = 2

n - 2 = 10

n = 12

Let x be the size of the exterior angle.

Then the interior angle size is 5x = 180-x degrees.

So 5x + x = 180, or 6x = 180, or x = 30 degrees. 5x = 180-x = 150 degrees.

Since the sum of the exterior angles of a polygon is 360 degrees,

the number of sides is 360/30 = 12 sides.

Let interior angle of polygon is x

Then exterior angle is x/5

thus , x+x/5=180⁰=6x/5

x= 150⁰

Exterior Angle is 30⁰

Sum of exterior angles of a polygon is 360⁰

30 x n = 360, n is number of sides of polygon

n=12

Answer 2

Answer :

• Polygon has 12 sides

Given :

• The exterior angle of a regular polygon is one - fifth of its interior angle

To find :

• How many sides have the polygon

Solution :

• Let the interior angle be x

Given that, The exterior angle of a regular polygon is one - fifth of its interior angle so,

• Exterior angle be 1/5x

We know that

Exterior angle for a regular polygon which say that

• Sum of adjacent interior and exterior angles is equal to 180⁰

➟ 1/5x + x = 180⁰

➟ x(1/5 + 1) = 180⁰

➟ x(6/5) = 180⁰

➟ x = 5/6 × 180⁰

➟ x = 5 × 30⁰

➟ x = 150⁰

• Interior angle = 150⁰
• Exterior angle = 1x/5 = 1(150)/5 = 150/5 = 30

Now Finding the how many sides does the polygon has?

We know that,

• 360⁰/Exterior angle

➟ 360⁰/30

➟ 12

Hence , Polygon has 12 sides