If the difference between the interior and exterior angles of a regular polygon is 144^{\circ}, then what is the number of sides of the polygon?

Explanation

Interior angle (I) + Exterior angle (E) = 180^{\circ} and I - E = 144^{\circ}. Subtracting gives 2E = 36^{\circ}, so E = 18^{\circ}. Number of sides n = \frac{360^{\circ}}{E} = \frac{360^{\circ}}{18^{\circ}} = 20.

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