Question

If each exterior angle of regular polygon are  36° , then how many sides does regular polygon have ?
1. 8
2. 10
3. 11
4. 12

Answer 1

Correct Answer - Option 2 : 10

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 + 36° = 180° 

⇒ angle of polygon = 144⁰ 

∴ 144 = \(\rm \left ( n-2 \right )\times \frac{180^{0}}{n}\)  

⇒ \(\rm \frac{4n}{5}= n-2\)  

⇒ n = 10 . 

The correct option is 2.