Question
Download Solution PDFIf each exterior angle of regular polygon are 24° , 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 + 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.
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