Question

The interior angles of a polygon are in Ap. The smallest angle is 52°and the common difference is 8°. Find the no. of sides of polygon.

Answer 1

Answer:the first angle given is 52

Other three will be in sum of 180-52

=128

So by creating AP

We could find this

a=52 d=8

Step-by-step explanation:

Answer 2

Answer:

Step-by-step explanation:

a=52,d=8

Sn=n/2(2(52)+(n-1)8)

n/2(104+8n-8)

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

And wkt,

(n-2)180-----(2). (to findinterior

sides a Of

polygon)

Now equate (1) and (2)

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

8n*2+96n=360n-720

8n*2+96n-360n+720=0

8n*2-264n+720=0(divide by 8)

n*2-33n+90=0

n*2-30n-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

I hope this answer may help you all