Which of the following is/are not the interior angle(s) of a regular polygon? I.108° II. 116°…

Explanation

Using the formula, \((n - 2) \times 180°\) to get the sum of the interior angles. Then we can have

\((n - 2) \times 180° = 108n\) ... (1)

\((n - 2) \times 180° = 116n\) ... (2)

\((n - 2) \times 180° = 120n\) ... (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° is not an angle of a regular polygon.