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Question
Calculate the number of sides of a regular polygon, if: the ratio between its exterior angle and interior angle is 2: 7.
Solution
Ratio between exterior angle and interior angle = 2: 7
Let exterior angle = 2x
Then interior angle = 7x
∴ 2x + 7x = 180°
⇒ 9x = 180°
`=> "x" = (180°)/9 = 20°`
∴ Ext. angle = 2x = 2 × 20° = 40°
∴ No. of. sides = `(360°)/40 = 9`
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