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In any polygon, the sum of the angles is given by the formula:

a = 180(n-2) where a = sum of angles and n = number of sides.

In a regular polygon (a shape where each angle and side is the same size / length), you can therefore work out that each angle is the total of the angles in the shape divided by the number of sides or:

a = 180(n-2)/n where a = size of the angle and n = number of sides

Alternatively, it is possible to work out the size of the angles by dividing 360 by the number of sides and subtracting from 180 or:

a = 180 - 360/n (letters as before)

This is because the external angles of a shape must equal 360 so the size of each is 360 divided by the number of sides. Therefore, the internal angle is 180 - the external angle.

NB: all answers are in degrees

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