If each exterior angle of regular polygon are  24° , then how many sides does regular polygon have ?

Concept:

Polygon of n sides, 

• Interior angle + exterior angle = 180°    
• Each interior angle of polygon = \(\rm \left ( n-2 \right )\times \frac{180^{0}}{n}\)  . 

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Calculation:

We know that ,  interior angle + exterior angle = 180° 

⇒ Interior angle + 24° = 180° 

⇒ interior angle of polygon = 1560 

∴ 156 = \(\rm \left ( n-2 \right )\times \frac{180^{0}}{n}\)  

⇒ 26n = 30n - 60

⇒  4n = 60

⇒ n = 15

The correct option is 3.