The number of sides of two regular polygons are in the ratio 5 4 The difference between their interi...........

Quantitative Aptitude (CDS) Coordinate Geometry

The number of sides of two regular polygons are in the ratio 5 : 4. The difference between their interior angles is 9^o. Consider the following statements :

1. One of them is a pentagon and the other is a rectangle.

2. One of them is a decagon and the other is an octagon.

3. The sum of their exterior angles is 720^o.

Which of the above statements is/are correct?

1 only

2 only

1 and 3

2 and 3

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Explanation:

Let the sides be 5x & 4x interior angle of regular polygon = ((n-2)180)/n

$\therefore \frac{(5x-2)180}{5x}- \frac{(4x-2)180}{4x} =9$

$= \frac{[(20x-8)-(20x-10)] 180}{20x}$

=> x = 2
Sides are 10 & 8
Hence, point 1 is wrong & point 2 is right.
Sum of exterior angles of any regular polygon is 360.
Hence, the sum of their exterior angles will be 360+360 = 720.
Hence, point 3 is also correct.