Question

If the interior angle of five-sided polygon are in the ratio 2 : 3 : 4 : 5 : 6, then find the difference between the largest and smallest angles.
1. 108° 
2. 104° 
3. 105° 
4. 110° 

Answer 1

Correct Answer - Option 1 : 108° 

Given:

The interior angle of five-sided polygon are in the ratio 2 : 3 : 4 : 5 : 6

Formula used:

Sum of all interior angles of a 'n' sided polygon = (n - 2) × 180° 

Calculation:

Sum of all interior angles of five sided polygon = (5 - 2) × 180° 

⇒ 540° 

Let all the angles are 2a, 3a, 4a, 5a, 6a respectively.

2a + 3a + 4a + 5a + 6a = 540

⇒ 20a = 540

⇒ a = 27

Largest angle = 6 × 27 = 162° 

Smallest angle = 2 × 27 = 54° 

Difference between them = 162° - 54° 

⇒ 108° 

∴ required difference is 108°