Polygonland

Here a = 120, d =5 . Let no. of sides be, n .

Then by geometry, sum of interior angles of the polygon = (2n - 4) $\times$ 90 .

Also, since the interior angles are in A.P.

so, there sum = $\frac { n }{ 2 } \left[ 2\times 120+\left( n-1 \right) 5 \right]$

equating both the equations, we get $\frac { n }{ 2 } \left[ 5n+235 \right] \quad =\quad \left( 2n-4 \right) 90$

on further solving, two values of n are 9 and 16.

But when n=16 ,

greatest interior angle, ${ t }_{ 16 }$ = a + 15d = 120 + 75 = 195 > 180

which is not possible,

$\therefore$ n = 9