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Consider the following statements. A) A regular polygon whose exterior angle between 75° and 85°. B) Ratio of interior angle to exterior angles having 5 sides of a polygon is 3 : 2. C) A polygon whose number of diagonals is 7. Which statement(s) is/are true?

Consider the following statements. A) A regular polygon whose exterior angle between 75° and 85°. B) Ratio of interior angle to exterior angles having 5 sides of a polygon is 3 : 2. C) A polygon whose number of diagonals is 7. Which statement(s) is/are true? Correct Answer Only B

Formula:

Each interior angle of having n sides regular polygon = /n

Each exterior angle of having n sides regular polygon = 360/n

Number of diagonals of having n sides regular polygon = /2

Calculation:

Each exterior angle of 4 sided regular polygon = 360/4 = 90

Each exterior angle of 5 sided regular polygon = 360/5 = 72

Each exterior angle of 6 sided regular polygon = 360/6 = 60

Now we can say there is no regular polygon whose exterior angle between 75 and 85.

Statement A is wrong.

Each exterior angle of 5 sided regular polygon = 360/5 = 72

Each interior angle of 5 sided regular polygon = /5 = 3 × 36 = 108

Ratio of interior angle to exterior angle = 108 : 72 = 3 : 2

Statement B is true.

Let number of side be n whose diagonals are 7.

n (n – 3)/2 = 7

⇒ n (n – 3) = 14

⇒ n2 – 3n – 14 = 0

n cannot be a whole number, so we can say statement C is wrong.

∴ Only statement B is true.

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