Using the formula, \((n - 2) \times 180^\circ\) to get the sum of the interior angles. Then we can have \((n - 2) \times 180^\circ = 108n\) ... (1) \((n - 2) \times 180^\circ = 116n\) ... (2) \((n - 2) \times 180^\circ = 120n\) ... (3) Solving the above given equations, where n is not a positive integer then that angle is not the interior for a regular polygon. (1): \(180n - 360 = 108n \implies 72n = 360\) \(n = 5\) (regular pentagon) (2): \(180n - 360 = 116n \implies 64n = 360\) \(n = 5.625\) (3): \(180n - 360 = 120n \implies 60n = 360\) \(n = 6\) (regular hexagon) Hence, 116^\circ is not an angle of a regular polygon.