Question

there are two regular polygons. one is having 3sides more than the other. Difference between their exterior angles is 6​

Answer 1

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8th

Maths

Understanding Quadrilaterals

Sum of Measures of Exterior Angles of a Polygon

The difference between the ...

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

∘

. Find the value of n.

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ANSWER

When number of sides of a regular polygon = n−1,

The value of its each exterior angle =

n−1

360

∘

When number of sides of a regular polygon = n+1,

The value of its each exterior angle =

n+1

360

∘

Given,

n−1

360

∘

−

n+1

360

∘

=9

∘

⇒360

∘

(n+1)−360

∘

(n−1)=9

∘

(n+1)(n−1)

⇒360

∘

[n+1−(n−1)]=9

∘

(n+1)(n−1)

⇒360

∘

(2)=9

∘

(n

2

−1)

⇒40

∘

(2)=n

2

−1

⇒80

∘

=n

2

−1

⇒n

2

=81

⇒n=9