Question

The interior angle of a regular polygon exceeds its exterior angle by 90°.The number of sides of the polygon is:
1. 6
2. 10
3. 8
4. 12

Answer 1

Correct Answer - Option 3 : 8

Given-   

The interior angle of a regular polygon exceeds its exterior angle by 90°

Concept Used-

Sum of interior angle and exterior angle of a regular polygon = 180°

Exterior angle of a regular polygon = 360/n     [where n = number of sides]

Calculation- 

Let the exterior angle of polygon be x and number of sides of polygon be n

According to Condition-

x + x + 90° = 180°

⇒ x = 45° 

Now,

45 = 360/n

⇒ n = 8

∴ The number of sides of the polygon is 8.