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