2018 · Q20
The number of sides of two regular polygons are in the ratio 5 : 4. The difference between their interior angles is 9°. Consider the following statements :
- 1One of them is a pentagon and the other is a rectangle.
- 2One of them is a decagon and the other is an octagon.
- 3The sum of their exterior angles is 720°.
Which of the above statements is/are correct ?
Elementary MathematicsQuadrilaterals and Polygons
- A1 only
- B2 only
- C1 and 3
- D2 and 3
Explanation
With sides 5n and 4n, the interior-angle difference is 180 x 2 x (1/(4n) - 1/(5n)) = 18/n = 9 degrees, so n = 2: a decagon and an octagon (statement 2 true; a rectangle is not a regular polygon, so statement 1 is false). The exterior angles of any polygon sum to 360 degrees, so two polygons give 720 degrees (statement 3 true). Hence option D.