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Mathematics

Assertion (A) : It is possible to have a regular polygon the sum of whose interior angle is 1000°.

Reason (R) : The sum of the interior angle of a polygon with n sides = (2n - 4) x 90°.

  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

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

S = (n - 2) x 180°

= (n - 2) x 2 x 90°

= (2n - 4) x 90°.

So, reason (R) is true.

If the sum of the interior angles is 1000°, let the polygon have n sides. Substituting this into the formula :

⇒ 1000° = (n - 2) x 180°

⇒ 1000° = 180°n - 360°

⇒ 180°n = 1000° + 360°

⇒ 180°n = 1360°

⇒ n = 1360°180°\dfrac{1360°}{180°}

⇒ n = 7.55…..

Since, n must be a whole number, there is no integer value of n that satisfies this equation.

So, assertion (A) is false.

∴ A is false, but R is true.

Hence, option 4 is the correct option.

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