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The difference between the exterior angles of the two regular polygons, having the sides equal to (n - 1) and (n + 1) is 9°. Find the value of n.
1. 9
2. 6
3. 7
4. 8

1 Answer

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Correct Answer - Option 1 : 9

Given

The difference between the exterior angles of the two regular polygons, having the sides equal to (n - 1) and (n + 1) is 9°

Concept

Sum of each each exterior angle = (360°/n)

Calculation

⇒ When number of sides of a regular polygon = (n - 1)

⇒ Each exterior angle = (360°/(n - 1))

⇒ When number of sides of a regular polygon = (n + 1)

⇒ Each exterior angle = (360°/(n + 1))

Now,

Difference is 

⇒ [(360°/(n - 1)) - (360°/(n + 1))] = 9° 

As 360° is common so take it out 

⇒ 360° × [(1/(n -1)) - (1/(n + 1))] = 9° 

⇒ [(n + 1 - n + 1)/(n2 - 12)] = (9°/360°)

⇒ (2/(n2 - 1)) = (1/40)

⇒ n2 - 1 = 80 

⇒ n2 = 81 

⇒ n = 9

∴ Number of side is 9

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