Question

The number of sides in two regular polygon are as 5:4 and the difference between their angle is 9 degree find the number of sides in polygon

Answer 1

Step-by-step explanation:

If a polygon has 'n' sides --

Each interior angle of a polygon = (n-2)180 / n

Let the first polygon has '5x' sides

So, the second one will have '4x' sides

So, eah interior angle of the first polygon = (n-2)180 / n = (5x-2)180 / 5x

Similarly, each interior angle of the second polygon = (n-2)180 / n = (4x -2)180 / 4x

Now, the difference between their interior angles is 9

So, (5x-2)180 / 5x - (4x-2)180 / 4x = 9

(900x - 360) / 5x - (720x - 360) / 4x = 9

[ 4(900x - 360) - 5(720x - 360) ] / 20x = 9

3600x - 1440 - 3600x + 1800 = 180x

360 = 180x

x = 2

So, the first polygon will have 5x = 5 × 2 = 10 sides and the second one will have 4x = 4 × 2 = 8 sides

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