Questions
The internal angles of a convex polygon are in A.P. The smallest angle is and the common difference is ,then number of sides of the polygon is
a
8
b
9
c
10
d
16
detailed solution
Correct option is B
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=9Talk to our academic expert!
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