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Use the formula for one interior angle of a regular n-sided polygon:



Therefore one exterior angle = 180° - 140° = 40°

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⇒ n² - 3n − 70 = 0

Now we need to solve that quadratic equation.
It can be factored into this: (n − 10)(n + 7) = 0
With solutions n = 10 or n = -7
n must be positive, so n = 10

The polygon has 10 sides

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Use the formula

with Radius = 10 cm and n = 9

= 20 cm × sin(0.3490...)
= 20 cm × 0.3420...
= 6.84 cm correct to 2 decimal places