Question

The sum of interior angle of a regular polygon is twice the sum of its exterior angles. Find the sum of interior angle of the polygon.
1. 720° 
2. 1080° 
3. 540° 
4. 900° 

Answer 1

Correct Answer - Option 1 : 720° 

Given

The sum of interior angle of a regular polygon is twice the sum of its exterior angles

Concept 

Sum of all interior angle = (n - 2) × 180° 

Sum of all exterior angle = 360° 

Calculation

⇒ (n - 2) × 180° = 2 × 360° 

⇒ (n - 2) = (720/180)

⇒ (n - 2) = 4 

⇒ n = 6 

Now, 

⇒ Sum of interior angle = (6 - 2) × 180° 

⇒ Sum of interior angle = 720° 

∴ Sum of interior angle = 720°