Question
Download Solution PDFIf each exterior angle of regular polygon are 36° , then how many sides does regular polygon have ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Polygon of n sides,
- Interior angle + exterior angle = 180°
- Each interior angle of polygon = \(\rm \left ( n-2 \right )\times \frac{180^{0}}{n}\) .
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.
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