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Question
The exterior angle of a regular polygon is one-third of its interior angle. Find the number of sides in the polygon.
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Solution
Let interior angle = x°
Exterior angle =`1/3` x°
`therefore "x" + 1/3 "x" = 180^circ`
3x + x = 540
4x = 540
x = `540/4`
x = 135°
∴ Exterior angle = `1/3 xx 135^circ = 45^circ`
Let no.of. sides = n
∵ each exterior angle = `360^circ/"n"`
∴ 45° = `(360°)/"n"`
∴ n = `(360°)/(45°)`
n = 8
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