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
Correct Answer: Option B
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.

Related:  If the 3rd and the 5th terms of an A.P are 6 and 10 respectively,...