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Answer

9

Explanation

Since, angle of polygon are in an AP.
`:.` Sum of all angles
`= (n -2) xx 180^(@) = (n)/(2) {2(120^(@)) + (n _1) 5^(@)}`
`rArr 5n^(2) - 125 n + 720 = 0`
`rArr n^(2) - 25n + 144 = 0`
`rArr (n -9) (n-16) = 0`
`rArr n = 9, 16`
If n = 9, then largest angle `= a + 8d = 160^(@)`
Again, if n = 16, then n largest angle
`= a + 15d = 120^(@) + 75 = 195^(@)`
Which is not possible.
[since, any angle of polygon cannot be `gt 180^(@)`]
Hence, n = 9 [neglecting n = 16]