Question

the difference between any two interior angles of a polygon is5°.if the smallest angle is 120°,find the number of sides of the polygon. ​

Answer 1

Answer:

16 or 9

Step-by-step explanation:

smallest angle = 120 ,d = 5

A.P - 120,125,130,135...

a = 120

sum of interior angles of ∆ = (n-2)×180

(n - 2)×180 = n/2[2a + (n-1)d ]

180n-360 = n/2 [2(120) + (n-1)5]

360n - 720 = 240n + 5n^2 - 5n

5n^2 - 125n + 720 = 0

5(n^2 - 25n + 144) = 0

n^2 - 25n + 144 = 0

n^2 - 16n - 9n + 144 = 0

n(n - 16) - 9( n - 16) = 0

n = 16 or 9

Answer 2

Answer:

hope it helps you ✌ ✌✌✌✌✌✌✌