Question

if the difference between the exterior angle of a n sided polygon and n+1 sided polygon is 6, Find the value of n​

Answer 1

Step-by-step explanation:

When number of sides of a regular polygon = n, 

The value of its each exterior angle = n360∘

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

The value of its each exterior angle = n+1360∘

Given n360∘−n+1360∘=12∘

 

⇒360∘(n+1)−360∘(n)=12∘(n+1)n

⇒360∘[n+1−n]=12∘(n2+n)

⇒360∘=12∘(n2+n)

⇒30∘=n2+n

⇒n2+n−30=0

⇒(n+6)(n−5)=0

⇒n=5 or  n=−6

Since, n can't  be negative.

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Answer 2

Step-by-step explanation:

When number of sides of a regular polygon = n,

The value of its each exterior angle =

n

360

∘

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

The value of its each exterior angle =

n+1

360

∘

Given

n

360

∘

−

n+1

360

∘

=12

∘

⇒360

∘

(n+1)−360

∘

(n)=12

∘

(n+1)n

⇒360

∘

[n+1−n]=12

∘

(n

2

+n)

⇒360

∘

=12

∘

(n

2

+n)

⇒30

∘

=n

2

+n

⇒n

2

+n−30=0

⇒(n+6)(n−5)=0

⇒n=5 or n=−6

Since, n can't be negative.

∴n=5