Question

1
10. The angles of a polygon are in A.P. with
common difference 5°. If the smallest angle
is 120°, find the number of sides of the
polygon.​

Answer 1

Answer:

Sum of interior angles =(n−2)×180

for n sides

⇒ n/2 (2a+(n−1)d)

⇒ n/2(2×120+(n−1)×5 )=(n−2)×180

⇒ n/2(240+5n−5)=180n−360

⇒240n+5n^2 −5n=360n−720

⇒5n^2−125n+720=0

⇒n^2−25n+144=0

n=16,9.