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Since the amount of sides of a polygon is equal to the amount of angles, we have:

144x = total angles

The total measure of each angle is determined by 180(x - 2), by splitting it into several triangles. Thus:

144x = 180(x - 2)

144x = 180x - 360

360 = 36x

x = 10

This polygon has 10 sides (a decagon).

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