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

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

Which of the following is/are not the interior angle(s) of a regular polygon? I.108° II. 116° III. 120°

• A.
I only
• B.
II only
• C.
III only
• D.
I and III only
##### 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.

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