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Mathematics

Assertion (A) : The sum of the interior angle of a regular polygon is thrice the sum of its exterior angle. The polygon is called an octagon.

Reason (R) : Each interior angle of a regular polygon = (n−2)×180°n\dfrac{(n - 2) \times 180°}{n}.

  1. Both A and R are correct, and R is the correct explanation for A.

  2. Both A and R are correct, and R is not the correct explanation for A.

  3. A is true, but R is false.

  4. A is false, but R is true.

Geometrical Shapes

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Answer

Given, the sum of the interior angle of a regular polygon is thrice the sum of its exterior angle.

The sum (S) of the interior angles of a polygon with n sides is given by the formula :

S = (n - 2) x 180°

The sum of the exterior angles = 360°

The sum of the interior angle = 3 x The sum of the exterior angles

⇒ (n - 2) x 180° = 3 x 360°

⇒ (n - 2) x 180° = 1080°

⇒ n - 2 = 1080°180°\dfrac{1080°}{180°}

⇒ n - 2 = 6

⇒ n = 6 + 2

⇒ n = 8

Thus, the polygon is octagon.

So, assertion (A) is true.

The sum of the interior angles of a polygon with n sides is given by the formula :

S = (n - 2) x 180°

Since, in a regular polygon each interior angle is equal.

∴ Each interior angle = Sn=(n−2)×180°n\dfrac{S}{n} = \dfrac{(n - 2) \times 180°}{n}

So, reason (R) is true.

∴ Both A and R are correct, and R is not the correct explanation for A.

Hence, option 2 is the correct option.

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