Question

Statement (1): The sum of the interior angles of a regular polygon is twice the sum of its exterior angles. The number of sides in the polygon is 6.

Statement (2): (2n − 4) × 90° = 2 × 360°

पर्याय

• Both the statements are true.

• Both the statements are false.

• Statement 1 is true, and statement 2 is false.

• Statement 1 is false, and statement 2 is true.

Answer 1

Both the statements are true.

Explanation:

• Statement (1): The sum of the interior angles of an n-sided polygon is given by (n − 2) × 180°, which is equivalent to (2n − 4) × 90°, and the sum of its exterior angles is always 360°. Setting the interior angle sum equal to twice the exterior angle sum gives:
  (2n − 4) × 90° = 2 × 360°
  (2n − 4) × 90° = 720°
  2n − 4 = 8
  2n = 12
  n = 6
  Thus, Statement (1) is true.
• Statement (2): The equation (2n − 4) × 90° = 2 × 360° directly represents the mathematical condition stated in Statement (1), making Statement (2) true as well.