The internal angles of a convex polygon are in A.P.  The smallest angle is 1200 and the common difference is 50 ,then number of sides of the polygon is

From geometry , the sum of all internal angles=(n−2)×1800 Where n is the number of sides of the polygon.∴n2[2×1200+(n−1)×50]=(n−2)×1800 ⇒n2−25n+144=0⇒(n−16)(n−9)=0 If n=16 then the 16th  internalAngle =1200+(16−1)×50=1950>1800 ∴n≠16 . Hence n=9