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Mathematics

Assertion (A): In a regular polygon, sum of its interior angles : sum of its external angles is 3 : 1. The number of sides (n) in it is 8.

Reason (R): (2n−4)×90°360°=31\dfrac{(2n - 4)\times 90°}{360°}=\dfrac{3}{1}

⇒ 2n−44=3 and n=8\dfrac{2n - 4}{4} = 3 \text{ and } n = 8

  1. A is true, R is false.
  2. A is false, R is true.
  3. Both A and R are true.
  4. Both A and R are false.

Rectilinear Figures

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Answer

Both A and R are true.

Explanation

Let the regular polygon has n number of sides.

Sum of interior angles of an n sided polygon = Sinterior = (2n - 4) x 90°

Sum of exterior angles of an n sided polygon = Sexterior = 360°

SinteriorSexterior=31⇒(2n−4)×90°360°=31⇒(2n−4)×90°=3×360°⇒180°n−360°=1080°⇒180°n=1080°+360°⇒180°n=1440°⇒n=1440°180°⇒n=8\dfrac{S{interior}}{S{exterior}} = \dfrac{3}{1}\\[1em] ⇒ \dfrac{(2n - 4) \times 90°}{360°} = \dfrac{3}{1}\\[1em] ⇒ (2n - 4) \times 90° = 3 \times 360°\\[1em] ⇒ 180°n - 360° = 1080°\\[1em] ⇒ 180°n = 1080° + 360° \\[1em] ⇒ 180°n = 1440° \\[1em] ⇒ n = \dfrac{1440°}{180°} \\[1em] ⇒ n = 8

∴ Assertion (A) is true.

From assertion, n = 8.

∴ Reason (R) is true.

Hence, both Assertion (A) and Reason (R) are true.

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