Mathematics
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) x 90° = 2 x 360°.
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.
Rectilinear Figures
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Answer
Sum of all exterior angles of any polygon (regular or irregular) is always 360°.
Sum of all interior angles of an n-sided polygon (regular or irregular) is (n - 2) x 180°.
It is given that the sum of interior angles of a regular polygon is twice the sum of its exterior angles.
⇒ (n - 2) x 180° = 2 x 360°
⇒ (n - 2) x 180° = 720°
⇒ 180°n - 360° = 720°
⇒ 180°n = 720° + 360°
⇒ 180°n = 1080°
⇒ n = = 6
Thus, the number of sides is 6.
As,
⇒ (n - 2) x 180° = 2 x 360°
⇒ (2n - 4) x 90° = 2 x 360°.
∴ Both the statements are true.
Hence, option 1 is the correct option.
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Statement 2: The number of diagonals through a vertex of a polygon = The number of sides in the polygon - 3.
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Assertion (A): If the diagonals of a quadrilateral bisect each other at right angles, then the quadrilateral is a rhombus.
Reason (R): A quadrilateral whose diagonals bisect each other at right angles must be a square.
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Both A and R are true, and R is the correct reason for A.
Both A and R are true, and R is the incorrect reason for A.