Question

The sum of the interior angles of a polygon is three times the sum of its exterior angles. Determine number of sides of the polygon .​

Answer 1

Answer:

As we know the sum of interior angles of a regular polygon =(n−2)×180∘, where n is the number of sides. Now it is given that the sum of interior angles of a polygon is three times the sum of exterior angles. Therefore sum of interior angles of a regular polygon = 3× sum of exterior angles.

Answer 2

Step-by-step explanation:

Given:

The sum of the interior angles of a polygon is three times the sum of its exterior angles.

To find:

Number of sides of the polygon.

Solution:

We know,

• Sum of exterior angles = 360

We have,

• Sum of interior angles = 3 x 360
• Sum of interior angles = 1080

Since,

Sum of interior angles of a polygon:

• (n - 2) x 180

Where,

• n = number of sides

Hence,

⇒ (n - 2) 180 = 1080

⇒ 180n - 360 = 1080  

⇒ 180n = 1440

⇒ n = 1440/180

⇒ n = 8

∴ The number of sides of the polygon are 8.