Question

the interior angles of a polygon are in AP smallest angle is 52 and the common difference is 8 find the number of sides​

Answer 1

Answer:

Step-by-step explanation:

Smallest angle (a)=52°

Difference (d)=8°

No of angles(n)=?

Sum of interior angles=

180(n-2)=n/2{2a+(n-1)d}

180(n-2)=n/2{2×52°+(n-1)8}

180(n-2)=n/2×2{52°+(n-1)4}

180(n-2)=n{52+4n-4}

180(n-2)=n{48+4n}

180n-360=48n+4n^2

4n^2+48n-180n+360=0

4n^2-132n+360=0

4{n^2-33n+90}=0

{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-30=0

N=3 / n=30 ans