Question

The difference between an interior angle of (N-1) sided polygon and an interior angle of(n+1) sided polygon is 6°. Find the value of n

Answer 1

Answer

An exterior angle of (n−1) sided regular polygon =

(n−1)

360

o

An exterior angle of (n+2) sided regular polygon =

(n+2)

360

o

Their difference is 6

o

So,

(n−1)

360

o

−

(n+2)

360

o

=6

o

=>60

(n−1)(n+2)

(n+2)−(n−1)

=1

=>(n−1)(n+2)=180

=>n

2

+n−2=180

=>n

2

+n−182=0

=>n

2

+14n−13n−182=0

=>(n−13)(n−14)=182

=>n=13,−14

Since n should be a positive number. So,n=13