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I have used the formulae $(n-2) \times 180^{\circ}$ and I have tried to work in algebra but I just can't do it

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Exterior angles (in a regular polygon) add to 360°. So you would do $360/40$ to get an answer of 9.

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That is not the fastest solution, but your $(n-2)\times 180^\circ$ is the sum of the interior angles.

Since the polygon is regular, each interior angle is therefore $\dfrac{n-2}{n}\times 180^\circ$. This should be equal to $180^\circ - 40^\circ$ so you can write an equation and solve for $n$.

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A regular polygon with an exterior angle measure of 40 degrees has nine sides. Every polygon's exterior angle sum equals 360. So 360/40 equals nine.

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