2018 · Q81
Given that the angles of a polygon are all equal and each angle is a right angle.
Statement 1The polygon has exactly four sides.
Statement 2The sum of the angles of a polygon having n sides is (3n - 8) right angles.
Which one of the following is correct in respect of the above statements?
Elementary MathematicsQuadrilaterals and Polygons
- ABoth Statement-1 and Statement-2 are true and Statement-2 is the correct explanation of Statement-1
- BBoth Statement-1 and Statement-2 are true but Statement-2 is not the correct explanation of Statement-1
- CStatement-1 is true but Statement-2 is false
- DStatement-1 is false but Statement-2 is true
Explanation
Statement-1 is true: an equiangular polygon with all right angles is a rectangle (four sides). Statement-2 is false: the angle sum is (n − 2) × 180° = (2n − 4) right angles, which equals (3n − 8) only for n = 4. Hence S1 true, S2 false, option (C).