Question

Interior angles of a polygon are in A.P. Smallest interior angle is ${52}^{\circ }$ and difference of consecutive interior angles is $8^{\circ }$, then find number of sides of the polygon.

Answer 1

a=52,d=8

Sₙ=n/2(2(52)+(n-1)8)

n/2(104+8n-8)

n/2(96+8n)---(1)

And we know that

(n-2)180-----(2).

sides a Of polygon

Now equate (1) and (2)

n/2(96+8n)=(n-2)180

8n²+96n=360n-720

8n²+96n-360n+720=0

8n²-264n+720=0(divide by 8)

n²-33n+90=0

n²-30n-3n+90=0

n(n-30)-3(n-30)=0

(n-3)(n-30)=0

n-3=0

n=3

And

n-30=0

n=30

As 'n's can't be more then 9,So

n=3

Therefore ,number of sides in polygon is 3